200 ejercicios de series resueltos paso a paso.

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Series
Hallar el resultado de la suma de las siguientes series:
1). (−5i + 8) =∑
i=1
65
2). ( i − ) =∑
i=1
56
−39
2
10
3
3). ( i − ) =∑
i=1
100 8
3
28
5
4). ( i + 12) =∑
i=1
64 −23
5
5). ( i − 2) =∑
i=1
71 −38
9
6). ( i + ) =∑
i=1
64 41
3
43
9
7). ( i + ) =∑
i=1
88 17
9
8
9
8). ( i − ) =∑
i=1
87 41
2
32
3
9). (7i − 3) =∑
i=1
56
10). ( i + ) =∑
i=1
88 38
3
46
5
11). ( i − ) =∑
i=1
77 43
5
45
8
12). (10i + 15) =∑
i=1
82
13). ( i + ) =∑
i=1
84 −1
10
41
5
14). ( i − ) =∑
i=1
99 −44
9
13
8
15). ( i + 8) =∑
i=1
100 31
7
16). ( i + ) =∑
i=1
89 19
3
4
5
17). ( i + ) =∑
i=1
61 28
5
5
6
18). ( i − ) =∑
i=1
71 15
8
17
3
19). ( i − ) =∑
i=1
73
−17
5
10
9
20). (−18i + ) =∑
i=1
83 1
2
21). ( i + ) =∑
i=1
100 1
5
38
7
22). (7i − 5) =∑
i=1
55
23). ( i + ) =∑
i=1
53 35
8
43
5
24). ( i − ) =∑
i=1
60
−12
7
19
6
25). ( i − ) =∑
i=1
90 −49
9
14
5
26). ( i − ) =∑
i=1
79 −27
8
11
9
27). ( i − ) =∑
i=1
97 −5
2
33
8
28). (−9i − ) =∑
i=1
63 29
2
29). (−3i − 14) =∑
i=1
69
30). ( i − ) =∑
i=1
65 −14
9
13
2
31). ( i − ) =∑
i=1
71
−39
5
1
9
32). ( i − 8) =∑
i=1
99
−5
2
33). ( i + ) =∑
i=1
95
−37
10
5
2
34). ( i − ) =∑
i=1
69 37
8
33
7
35). (−7i − ) =∑
i=1
50 34
9
36). (2i − ) =∑
i=1
85 7
3
37). ( i + ) =∑
i=1
59 37
2
22
3
38). ( i + ) =∑
i=1
57 −43
10
13
5
39). ( i + ) =∑
i=1
56 3
2
8
7
40). (−4i − ) =∑
i=1
50 13
7
41). (−2i − 11) =∑
i=1
63
42). ( i − ) =∑
i=1
54 −32
9
26
7
43). ( i − 3) =∑
i=1
65
−7
3
44). ( i + ) =∑
i=1
81 1
3
35
9
45). (3i + ) =∑
i=1
92 49
9
46). ( i − ) =∑
i=1
59 −4
3
35
2
47). ( i − ) =∑
i=1
93 −41
10
7
4
48). ( i − ) =∑
i=1
84 −21
8
47
7
49). ( i − ) =∑
i=1
69 −39
7
22
5
50). (15i − ) =∑
i=1
56 19
2
51). ( i + 11) =∑
i=1
100 44
5
52). ( i + ) =∑
i=1
62
−11
2
29
7
53). ( i − 2) =∑
i=1
97 11
2
54). ( i + ) =∑
i=1
90
−3
10
6
5
55). ( i + ) =∑
i=1
66 −45
2
17
5
56). ( i + ) =∑
i=1
74 −5
2
16
5
57). ( i − 2) =∑
i=1
83 −37
7
58). ( i − ) =∑
i=1
90 1
2
7
2
59). ( i − ) =∑
i=1
64 −25
4
31
5
60). ( i − ) =∑
i=1
51 −16
3
3
10
61). ( i − 3) =∑
i=1
78 −31
9
62). ( i + ) =∑
i=1
60 5
3
5
3
63). ( i − 4) =∑
i=1
66 −15
7
64). (−6i − ) =∑
i=1
93 5
8
65). ( i − 9) =∑
i=1
61
−25
7
66). (6i + ) =∑
i=1
69 17
4
67). −7i =∑
i=1
63
68). ( i − ) =∑
i=1
76 35
3
17
7
69). (−7i + ) =∑
i=1
67 3
2
70). ( i − ) =∑
i=1
81 −23
4
47
10
71). ( i − 9) =∑
i=1
100 −1
2
72). ( i + ) =∑
i=1
76 49
2
9
7
73). ( i − ) =∑
i=1
70 1
10
40
9
74). ( i − ) =∑
i=1
57
−24
7
11
6
75). (−4i − ) =∑
i=1
51 1
5
76). ( i − 3) =∑
i=1
95 27
5
77). ( i − ) =∑
i=1
86 11
3
17
5
78). ( i + ) =∑
i=1
72 −9
5
11
4
79). (5i − ) =∑
i=1
73 31
2
80). ( i − ) =∑
i=1
91 23
5
25
9
81). (−2i − ) =∑
i=1
96 45
7
82). ( i − ) =∑
i=1
82 −31
5
31
4
83). ( i + ) =∑
i=1
91 45
8
13
5
84). ( i − 2) =∑
i=1
79 −9
4
85). ( i − ) =∑
i=1
77 44
3
15
7
86). ( i − ) =∑
i=1
57 7
3
24
5
87). ( i − ) =∑
i=1
88
−12
5
2
3
88). ( i + 8) =∑
i=1
69 −17
10
89). ( i − ) =∑
i=1
56 45
4
37
5
90). ( i − 23) =∑
i=1
97 −2
3
91). ( i − ) =∑
i=1
79 25
7
37
6
92). ( i − ) =∑
i=1
51 22
3
1
2
93). ( i + ) =∑
i=1
95 13
8
9
2
94). (−3i − ) =∑
i=1
65 1
5
95). ( i − ) =∑
i=1
67 29
6
2
5
96). ( i + ) =∑
i=1
78
−22
3
44
7
97). ( i − ) =∑
i=1
72
−24
7
43
8
98). ( i + ) =∑
i=1
79 47
7
5
2
99). (−4i + ) =∑
i=1
51 37
7
100). (4i − ) =∑
i=1
93 25
9
101). ( i − ) =∑
i=1
100 4
5
25
9
102). ( i + ) =∑
i=1
64 27
7
50
3
103). ( i + ) =∑
i=1
97
−47
4
13
3
104). ( i − ) =∑
i=1
77 11
9
9
10
105). (−24i − ) =∑
i=1
90 14
5
106). ( i − ) =∑
i=1
72 19
9
46
5
107). (−2i + ) =∑
i=1
88 43
4
108). ( i + ) =∑
i=1
58 18
5
26
9
109). (−4i + ) =∑
i=1
56 10
7
110). (−20i − ) =∑
i=1
62 13
3
111). ( i + ) =∑
i=1
88 28
5
25
7
112). ( i − ) =∑
i=1
52 5
2
10
7
113). ( i − ) =∑
i=1
74 46
7
14
5
114). ( i + 4) =∑
i=1
78 −8
7
115). ( i + 1) =∑
i=1
70
−3
5
116). ( i − ) =∑
i=1
87
−3
5
49
9
117). ( i − ) =∑
i=1
69
−37
10
17
10
118). ( i − 5) =∑
i=1
87 −17
2
119). ( i − ) =∑
i=1
101 −7
5
16
7
120). ( i + ) =∑
i=1
69 17
5
31
9
121). (3i + ) =∑
i=1
99 47
3
122). (−8i + ) =∑
i=1
59 18
5
123). (−8i + ) =∑
i=1
99 19
6
124). (12i + 3) =∑
i=1
83
125). ( i − 2) =∑
i=1
56 23
4
126). ( i − ) =∑
i=1
80
−47
5
13
2
127). ( i − ) =∑
i=1
54 −17
4
23
8
128). ( i − ) =∑
i=1
91 4
7
1
3
129). (6i − 22) =∑
i=1
76
130). ( i + 6) =∑
i=1
87 −9
5
131). ( i − 10) =∑
i=1
98 1
7
132). (−7i + 10) =∑
i=1
90
133). ( i − 1) =∑
i=1
98 −12
5
134). ( i + 3) =∑
i=1
98 29
7
135). ( i − ) =∑
i=1
50 −43
10
5
2
136). ( i − ) =∑
i=1
62 26
7
8
3
137). (9i + ) =∑
i=1
96 7
2
138). ( i + ) =∑
i=1
90 1
3
4
3
139). (−15i + ) =∑
i=1
85 41
9
140). ( i + ) =∑
i=1
51 49
10
23
3
141). ( i − ) =∑
i=1
88 −16
9
45
7
142). ( i + ) =∑
i=1
68 −25
3
7
2
143). ( i + ) =∑
i=1
63 −29
8
23
6
144). ( i − ) =∑
i=1
50 16
3
11
4
145). ( i + ) =∑
i=1
83
−3
2
41
6
146). ( i + 3) =∑
i=1
94
−47
2
147). (10i + ) =∑
i=1
73 1
2
148). ( i − ) =∑
i=1
80 42
5
41
8
149). ( i − ) =∑
i=1
95 11
7
39
5
150). ( i + ) =∑
i=1
67
−1
3
11
4
151). ( i + ) =∑
i=1
91 −1
7
27
8
152). ( i + ) =∑
i=1
94 10
7
2
7
153). ( i − ) =∑
i=1
57 −38
5
39
7
154). ( i − ) =∑
i=1
83
−43
7
17
7
155). ( i − ) =∑
i=1
101 27
7
13
5
156). ( i − ) =∑
i=1
88 27
7
1
2
157). ( i − ) =∑
i=1
91 17
7
1
2
158). ( i + ) =∑
i=1
55 17
5
14
3
159). ( i − ) =∑
i=1
55 −7
2
19
6
160). ( i − ) =∑
i=1
50 32
7
31
3
161). ( i + ) =∑
i=1
70 49
6
8
5
162). ( i + ) =∑
i=1
96 1
4
3
7
163). (−8i + ) =∑
i=1
77 37
7
164). (−6i − ) =∑
i=1
79 23
7
165). ( i − 2) =∑
i=1
88 8
5
166). ( i + ) =∑
i=1
89 1
9
25
3
167). ( i + 16) =∑
i=1
51
−33
2
168). ( i + ) =∑
i=1
86
−15
7
34
5
169). ( i − ) =∑
i=1
68 22
5
39
4
170). ( i − ) =∑
i=1
100 −23
5
25
3
171). ( i + ) =∑
i=1
78 16
5
14
5
172). ( i + ) =∑
i=1
66 −11
5
29
8
173). ( i + ) =∑
i=1
58 −3
4
4
3
174). ( i + ) =∑
i=1
94 7
6
26
3
175). (7i − ) =∑
i=1
78 5
9
176). ( i + 17) =∑
i=1
73
−13
3
177). ( i − ) =∑
i=1
53
−32
7
25
2
178). (−15i − ) =∑
i=1
93 11
5
179). ( i − ) =∑
i=1
77 −25
9
19
10
180). ( i + ) =∑
i=1
80 23
2
38
7
181). ( i − ) =∑
i=1
95 −38
3
26
7
182). ( i − ) =∑
i=1
61 −39
5
1
2
183). ( i − 10) =∑
i=1
89 18
5
184). (−i + 12) =∑
i=1
77
185). ( i − ) =∑
i=1
81 1
5
23
4
186). ( i + ) =∑
i=1
64 11
6
32
3
187). ( i + ) =∑
i=1
97 18
7
17
2
188). ( i − ) =∑
i=1
96 17
2
16
3
189). ( i − ) =∑
i=1
72
−8
9
27
2
190). ( i + ) =∑
i=1
53 −27
8
13
3
191). ( i + 4) =∑
i=1
91 19
9
192). ( i + ) =∑
i=1
70 17
6
1
5
193). ( i + ) =∑
i=1
50 −7
2
11
4
194). ( i + ) =∑
i=1
53 −17
2
36
7
195). ( i + ) =∑
i=1
61 19
5
37
9
196). ( i + ) =∑
i=1
75 9
5
19
2
197). (4i + 6) =∑
i=1
78
198). ( i + ) =∑
i=1
69 24
5
43
2
199). ( i + ) =∑
i=1
92 29
6
22
5
200). ( i − ) =∑
i=1
55
−16
5
47
2
HOJA DE RESPUESTAS
Series
Hallar el resultado de la suma de las siguientes series:
1).
2).
3).
4).
5).
6).
7).
(−5i + 8)∑
i=1
65
= −5i + 8 = −5 i + 8 1 = −5 ⋅ + 8 ⋅ 65∑
i=1
65
∑
i=1
65
∑
i=1
65
∑
i=1
65 65 ⋅ (65 + 1)
2
= −5 ⋅ 2145 + 8 ⋅ 65 = −10725 + 520 = −10205
( i − )∑
i=1
56
−39
2
10
3
= i − = i − 1∑
i=1
56
−39
2
∑
i=1
56 10
3
−39
2
∑
i=1
56 10
3
∑
i=1
56
= ⋅ − ⋅ 56 = ⋅ 1596 − ⋅ 56
−39
2
56 ⋅ (56 + 1)
2
10
3
−39
2
10
3
= −31122 − =
560
3
−93926
3
( i − )∑
i=1
100 8
3
28
5
= i − = i − 1∑
i=1
100 8
3
∑
i=1
100 28
5
8
3
∑
i=1
100 28
5
∑
i=1
100
= ⋅ − ⋅ 100 = ⋅ 5050 − ⋅ 100
8
3
100 ⋅ (100 + 1)
2
28
5
8
3
28
5
= − 560 =
40400
3
38720
3
( i + 12)∑
i=1
64 −23
5
= i +12 = i + 12 1 = ⋅ + 12 ⋅ 64∑
i=1
64 −23
5
∑
i=1
64 −23
5
∑
i=1
64
∑
i=1
64 −23
5
64 ⋅ (64 + 1)
2
= ⋅ 2080 + 12 ⋅ 64 = −9568 + 768 = −8800
−23
5
( i − 2)∑
i=1
71 −38
9
= i − 2 = i − 2 1 = ⋅ − 2 ⋅ 71∑
i=1
71 −38
9
∑
i=1
71 −38
9
∑
i=1
71
∑
i=1
71 −38
9
71 ⋅ (71 + 1)
2
= ⋅ 2556 − 2 ⋅ 71 = −10792 − 142 = −10934
−38
9
( i + )∑
i=1
64 41
3
43
9
= i + = i + 1∑
i=1
64 41
3
∑
i=1
64 43
9
41
3
∑
i=1
64 43
9
∑
i=1
64
= ⋅ + ⋅ 64 = ⋅ 2080 + ⋅ 64
41
3
64 ⋅ (64 + 1)
2
43
9
41
3
43
9
= + =
85280
3
2752
9
258592
9
( i + )∑
i=1
88 17
9
8
9
= i + = i + 1∑
i=1
88 17
9
∑
i=1
88 8
9
17
9
∑
i=1
88 8
9
∑
i=1
88
= ⋅ + ⋅ 88 = ⋅ 3916 + ⋅ 88
17
9
88 ⋅ (88 + 1)
2
8
9
17
9
8
9
= + =
66572
9
704
9
67276
9
8).
9).
10).
11).
12).
13).
14).
( i − )∑
i=1
87 41
2
32
3
= i − = i − 1∑
i=1
87 41
2
∑
i=1
87 32
3
41
2
∑
i=1
87 32
3
∑
i=1
87
= ⋅ − ⋅ 87 = ⋅ 3828 − ⋅ 87
41
2
87 ⋅ (87 + 1)
2
32
3
41
2
32
3
= 78474 − 928 = 77546
(7i − 3)∑
i=1
56
= 7i − 3 = 7 i − 3 1 = 7 ⋅ − 3 ⋅ 56∑
i=1
56
∑
i=1
56
∑
i=1
56
∑
i=1
56 56 ⋅ (56 + 1)
2
= 7 ⋅ 1596 − 3 ⋅ 56 = 11172 − 168 = 11004
( i + )∑
i=1
88 38
3
46
5
= i + = i + 1∑
i=1
88 38
3
∑
i=1
88 46
5
38
3
∑
i=1
88 46
5
∑
i=1
88
= ⋅ + ⋅ 88 = ⋅ 3916 + ⋅ 88
38
3
88 ⋅ (88 + 1)
2
46
5
38
3
46
5
= + =
148808
3
4048
5
756184
15
( i − )∑
i=1
77 43
5
45
8
= i − = i − 1∑
i=1
77 43
5
∑
i=1
77 45
8
43
5
∑
i=1
77 45
8
∑
i=1
77
= ⋅ − ⋅ 77 = ⋅ 3003 − ⋅ 77
43
5
77 ⋅ (77 + 1)
2
45
8
43
5
45
8
= − =
129129
5
3465
8
1015707
40
(10i + 15)∑
i=1
82
= 10i + 15 = 10 i + 15 1 = 10 ⋅ + 15 ⋅ 82∑
i=1
82
∑
i=1
82
∑
i=1
82
∑
i=1
82 82 ⋅ (82 + 1)
2
= 10 ⋅ 3403 + 15 ⋅ 82 = 34030 + 1230 = 35260
( i + )∑
i=1
84 −1
10
41
5
= i + = i + 1∑
i=1
84 −1
10
∑
i=1
84 41
5
−1
10
∑
i=1
84 41
5
∑
i=1
84
= ⋅ + ⋅ 84 = ⋅ 3570 + ⋅ 84
−1
10
84 ⋅ (84 + 1)
2
41
5
−1
10
41
5
= −357 + =
3444
5
1659
5
( i − )∑
i=1
99
−44
9
13
8
= i − = i − 1∑
i=1
99
−44
9
∑
i=1
99 13
8
−44
9
∑
i=1
99 13
8
∑
i=1
99
= ⋅ − ⋅ 99 = ⋅ 4950 − ⋅ 99
−44
9
99 ⋅ (99 + 1)
2
13
8
−44
9
13
8
= −24200 − =
1287
8
−194887
8
15).
16).
17).
18).
19).
20).
21).
( i + 8)∑
i=1
100 31
7
= i + 8 = i + 8 1 = ⋅ + 8 ⋅ 100∑
i=1
100 31
7
∑
i=1
100 31
7
∑
i=1
100
∑
i=1
100 31
7
100 ⋅ (100 + 1)
2
= ⋅ 5050 + 8 ⋅ 100 = + 800 =
31
7
156550
7
162150
7
( i + )∑
i=1
89 19
3
4
5
= i + = i + 1∑
i=1
89 19
3
∑
i=1
89 4
5
19
3
∑
i=1
89 4
5
∑
i=1
89
= ⋅ + ⋅ 89 = ⋅ 4005 + ⋅ 89
19
3
89 ⋅ (89 + 1)
2
4
5
19
3
4
5
= 25365 + =
356
5
127181
5
( i + )∑
i=1
61 28
5
5
6
= i + = i + 1∑
i=1
61 28
5
∑
i=1
61 5
6
28
5
∑
i=1
61 5
6
∑
i=1
61
= ⋅ + ⋅ 61 = ⋅ 1891 + ⋅ 61
28
5
61 ⋅ (61 + 1)
2
5
6
28
5
5
6
= + =
52948
5
305
6
319213
30
( i − )∑
i=1
71 15
8
17
3
= i − = i − 1∑
i=1
71 15
8
∑
i=1
71 17
3
15
8
∑
i=1
71 17
3
∑
i=1
71
= ⋅ − ⋅ 71 = ⋅ 2556 − ⋅ 71
15
8
71 ⋅ (71 + 1)
2
17
3
15
8
17
3
= − =
9585
2
1207
3
26341
6
( i − )∑
i=1
73
−17
5
10
9
= i − = i − 1∑
i=1
73
−17
5
∑
i=1
73 10
9
−17
5
∑
i=1
73 10
9
∑
i=1
73
= ⋅ − ⋅ 73 = ⋅ 2701 − ⋅ 73
−17
5
73 ⋅ (73 + 1)
2
10
9
−17
5
10
9
= − =
−45917
5
730
9
−416903
45
(−18i + )∑
i=1
83 1
2
= −18i + = −18 i + 1 = −18 ⋅ + ⋅ 83∑
i=1
83
∑
i=1
83 1
2
∑
i=1
83 1
2
∑
i=1
83 83 ⋅ (83 + 1)
2
1
2
= −18 ⋅ 3486 + ⋅ 83 = −62748 + =
1
2
83
2
−125413
2
( i + )∑
i=1
100 1
5
38
7
= i + = i + 1∑
i=1
100 1
5
∑
i=1
100 38
7
1
5
∑
i=1
100 38
7
∑
i=1
100
= ⋅ + ⋅ 100 = ⋅ 5050 + ⋅ 100
1
5
100 ⋅ (100 + 1)
2
38
7
1
5
38
7
= 1010 + =
3800
7
10870
7
22).
23).
24).
25).
26).
27).
28).
(7i − 5)∑
i=1
55
= 7i − 5 = 7 i − 5 1 = 7 ⋅ − 5 ⋅ 55∑
i=1
55
∑
i=1
55
∑
i=1
55
∑
i=1
55 55 ⋅ (55 + 1)
2
= 7 ⋅ 1540 − 5 ⋅ 55 = 10780 − 275 = 10505
( i + )∑
i=1
53 35
8
43
5
= i + = i + 1∑
i=1
53 35
8
∑
i=1
53 43
5
35
8
∑
i=1
53 43
5
∑
i=1
53
= ⋅ + ⋅ 53 = ⋅ 1431 + ⋅ 53
35
8
53 ⋅ (53 + 1)
2
43
5
35
8
43
5
= + =
50085
8
2279
5
268657
40
( i − )∑
i=1
60
−12
7
19
6
= i − = i − 1∑
i=1
60
−12
7
∑
i=1
60 19
6
−12
7
∑
i=1
60 19
6
∑
i=1
60
= ⋅ − ⋅ 60 = ⋅ 1830 − ⋅ 60
−12
7
60 ⋅ (60 + 1)
2
19
6
−12
7
19
6
= − 190 =
−21960
7
−23290
7
( i − )∑
i=1
90 −49
9
14
5
= i − = i − 1∑
i=1
90 −49
9
∑
i=1
90 14
5
−49
9
∑
i=1
90 14
5
∑
i=1
90
= ⋅ − ⋅ 90 = ⋅ 4095 − ⋅ 90
−49
9
90 ⋅ (90 + 1)
2
14
5
−49
9
14
5
= −22295 − 252 = −22547
( i − )∑
i=1
79
−27
8
11
9
= i − = i − 1∑
i=1
79
−27
8
∑
i=1
79 11
9
−27
8
∑
i=1
79 11
9
∑
i=1
79
= ⋅ − ⋅ 79 = ⋅ 3160 − ⋅ 79
−27
8
79 ⋅ (79 + 1)
2
11
9
−27
8
11
9
= −10665 − =
869
9
−96854
9
( i − )∑
i=1
97 −5
2
33
8
= i − = i − 1∑
i=1
97 −5
2
∑
i=1
97 33
8
−5
2
∑
i=1
97 33
8
∑
i=1
97
= ⋅ − ⋅ 97 = ⋅ 4753 − ⋅ 97
−5
2
97 ⋅ (97 + 1)
2
33
8
−5
2
33
8
= − =
−23765
2
3201
8
−98261
8
(−9i − )∑
i=1
63 29
2
= −9i − = −9 i − 1 = −9 ⋅ − ⋅ 63∑
i=1
63
∑
i=1
63 29
2
∑
i=1
63 29
2
∑
i=1
63 63 ⋅ (63 + 1)
2
29
2
= −9 ⋅ 2016 − ⋅ 63 = −18144 − =
29
2
1827
2
−38115
2
29).
30).
31).
32).
33).
34).
35).
36).
(−3i − 14)∑
i=1
69
= −3i − 14 = −3 i − 14 1 = −3 ⋅ − 14 ⋅ 69∑
i=1
69
∑
i=1
69
∑
i=1
69
∑
i=1
69 69 ⋅ (69 + 1)
2
= −3 ⋅ 2415 − 14 ⋅ 69 = −7245 − 966 = −8211
( i − )∑
i=1
65 −14
9
13
2
= i − = i − 1∑
i=1
65 −14
9
∑
i=1
65 13
2
−14
9
∑
i=1
65 13
2
∑
i=1
65
= ⋅ − ⋅ 65 = ⋅ 2145 − ⋅ 65
−14
9
65 ⋅ (65 + 1)
2
13
2
−14
9
13
2
= − =
−10010
3
845
2
−22555
6
( i − )∑
i=1
71
−39
5
1
9
= i − = i − 1∑
i=1
71
−39
5
∑
i=1
71 1
9
−39
5
∑
i=1
71 1
9
∑
i=1
71
= ⋅ − ⋅ 71 = ⋅ 2556 − ⋅ 71
−39
5
71 ⋅ (71 + 1)
2
1
9
−39
5
1
9
= − =
−99684
5
71
9
−897511
45
( i − 8)∑
i=1
99 −5
2
= i − 8 = i − 8 1 = ⋅ − 8 ⋅ 99∑
i=1
99 −5
2
∑
i=1
99 −5
2
∑
i=1
99
∑
i=1
99 −5
2
99 ⋅ (99 + 1)
2
= ⋅ 4950 − 8 ⋅ 99 = −12375 − 792 = −13167
−5
2
( i + )∑
i=1
95
−37
10
5
2
= i + = i + 1∑
i=1
95
−37
10
∑
i=1
95 5
2
−37
10
∑
i=1
95 5
2
∑
i=1
95
= ⋅ + ⋅ 95 = ⋅ 4560 + ⋅ 95
−37
10
95 ⋅ (95 + 1)
2
5
2
−37
10
5
2
= −16872 + =
475
2
−33269
2
( i − )∑
i=1
69 37
8
33
7
= i − = i − 1∑
i=1
69 37
8
∑
i=1
69 33
7
37
8
∑
i=1
69 33
7
∑
i=1
69
= ⋅ − ⋅ 69 = ⋅ 2415 − ⋅ 69
37
8
69 ⋅ (69 + 1)
2
33
7
37
8
33
7
= − =
89355
8
2277
7
607269
56
(−7i − )∑
i=1
50 34
9
= −7i − = −7 i − 1 = −7 ⋅ − ⋅ 50∑
i=1
50
∑
i=1
50 34
9
∑
i=1
50 34
9
∑
i=1
50 50 ⋅ (50 + 1)
2
34
9
= −7 ⋅ 1275 − ⋅ 50 = −8925 − =
34
9
1700
9
−82025
9
(2i − )∑
i=1
85 7
3
= 2i − = 2 i − 1 = 2 ⋅ − ⋅ 85∑
i=1
85
∑
i=1
85 7
3
∑
i=1
85 7
3
∑
i=1
85 85 ⋅ (85 + 1)
2
7
3
= 2 ⋅ 3655 − ⋅ 85 = 7310 − =
7
3
595
3
21335
3
37).
38).
39).
40).
41).
42).
43).
( i + )∑
i=1
59 37
2
22
3
= i + = i + 1∑
i=1
59 37
2
∑
i=1
59 22
3
37
2
∑
i=1
59 22
3
∑
i=1
59
= ⋅ + ⋅ 59 = ⋅ 1770 + ⋅ 59
37
2
59 ⋅ (59 + 1)
2
22
3
37
2
22
3
= 32745 + =
1298
3
99533
3
( i + )∑
i=1
57 −43
10
13
5
= i + = i + 1∑
i=1
57 −43
10
∑
i=1
57 13
5
−43
10
∑
i=1
57 13
5
∑
i=1
57
= ⋅ + ⋅ 57 = ⋅ 1653 + ⋅ 57
−43
10
57 ⋅ (57 + 1)
2
13
5
−43
10
13
5
= + =
−71079
10
741
5
−69597
10
( i + )∑
i=1
56 3
2
8
7
= i + = i + 1∑
i=1
56 3
2
∑
i=1
56 8
7
3
2
∑
i=1
56 8
7
∑
i=1
56
= ⋅ + ⋅ 56 = ⋅ 1596 + ⋅ 56
3
2
56 ⋅ (56 + 1)
2
8
7
3
2
8
7
= 2394 + 64 = 2458
(−4i − )∑
i=1
50 13
7
= −4i − = −4 i − 1 = −4 ⋅ − ⋅ 50∑
i=1
50
∑
i=1
50 13
7
∑
i=1
50 13
7
∑
i=1
50 50 ⋅ (50 + 1)
2
13
7
= −4 ⋅ 1275 − ⋅ 50 = −5100 − =
13
7
650
7
−36350
7
(−2i − 11)∑
i=1
63
= −2i − 11 = −2 i − 11 1 = −2 ⋅ − 11 ⋅ 63∑
i=1
63
∑
i=1
63
∑
i=1
63
∑
i=1
63 63 ⋅ (63 + 1)
2
= −2 ⋅ 2016 − 11 ⋅ 63 = −4032 − 693 = −4725
( i − )∑
i=1
54
−32
9
26
7
= i − = i − 1∑
i=1
54
−32
9
∑
i=1
54 26
7
−32
9
∑
i=1
54 26
7
∑
i=1
54= ⋅ − ⋅ 54 = ⋅ 1485 − ⋅ 54
−32
9
54 ⋅ (54 + 1)
2
26
7
−32
9
26
7
= −5280 − =
1404
7
−38364
7
( i − 3)∑
i=1
65 −7
3
= i − 3 = i − 3 1 = ⋅ − 3 ⋅ 65∑
i=1
65 −7
3
∑
i=1
65 −7
3
∑
i=1
65
∑
i=1
65 −7
3
65 ⋅ (65 + 1)
2
= ⋅ 2145 − 3 ⋅ 65 = −5005 − 195 = −5200
−7
3
44).
45).
46).
47).
48).
49).
50).
( i + )∑
i=1
81 1
3
35
9
= i + = i + 1∑
i=1
81 1
3
∑
i=1
81 35
9
1
3
∑
i=1
81 35
9
∑
i=1
81
= ⋅ + ⋅ 81 = ⋅ 3321 + ⋅ 81
1
3
81 ⋅ (81 + 1)
2
35
9
1
3
35
9
= 1107 + 315 = 1422
(3i + )∑
i=1
92 49
9
= 3i + = 3 i + 1 = 3 ⋅ + ⋅ 92∑
i=1
92
∑
i=1
92 49
9
∑
i=1
92 49
9
∑
i=1
92 92 ⋅ (92 + 1)
2
49
9
= 3 ⋅ 4278 + ⋅ 92 = 12834 + =
49
9
4508
9
120014
9
( i − )∑
i=1
59
−4
3
35
2
= i − = i − 1∑
i=1
59
−4
3
∑
i=1
59 35
2
−4
3
∑
i=1
59 35
2
∑
i=1
59
= ⋅ − ⋅ 59 = ⋅ 1770 − ⋅ 59
−4
3
59 ⋅ (59 + 1)
2
35
2
−4
3
35
2
= −2360 − =
2065
2
−6785
2
( i − )∑
i=1
93 −41
10
7
4
= i − = i − 1∑
i=1
93 −41
10
∑
i=1
93 7
4
−41
10
∑
i=1
93 7
4
∑
i=1
93
= ⋅ − ⋅ 93 = ⋅ 4371 − ⋅ 93
−41
10
93 ⋅ (93 + 1)
2
7
4
−41
10
7
4
= − =
−179211
10
651
4
−361677
20
( i − )∑
i=1
84 −21
8
47
7
= i − = i − 1∑
i=1
84 −21
8
∑
i=1
84 47
7
−21
8
∑
i=1
84 47
7
∑
i=1
84
= ⋅ − ⋅ 84 = ⋅ 3570 − ⋅ 84
−21
8
84 ⋅ (84 + 1)
2
47
7
−21
8
47
7
= − 564 =
−37485
4
−39741
4
( i − )∑
i=1
69 −39
7
22
5
= i − = i − 1∑
i=1
69 −39
7
∑
i=1
69 22
5
−39
7
∑
i=1
69 22
5
∑
i=1
69
= ⋅ − ⋅ 69 = ⋅ 2415 − ⋅ 69
−39
7
69 ⋅ (69 + 1)
2
22
5
−39
7
22
5
= −13455 − =
1518
5
−68793
5
(15i − )∑
i=1
56 19
2
= 15i − = 15 i − 1 = 15 ⋅ − ⋅ 56∑
i=1
56
∑
i=1
56 19
2
∑
i=1
56 19
2
∑
i=1
56 56 ⋅ (56 + 1)
2
19
2
= 15 ⋅ 1596 − ⋅ 56 = 23940 − 532 = 23408
19
2
51).
52).
53).
54).
55).
56).
57).
( i + 11)∑
i=1
100 44
5
= i + 11 = i + 11 1 = ⋅ + 11 ⋅ 100∑
i=1
100 44
5
∑
i=1
100 44
5
∑
i=1
100
∑
i=1
100 44
5
100 ⋅ (100 + 1)
2
= ⋅ 5050 + 11 ⋅ 100 = 44440 + 1100 = 45540
44
5
( i + )∑
i=1
62
−11
2
29
7
= i + = i + 1∑
i=1
62
−11
2
∑
i=1
62 29
7
−11
2
∑
i=1
62 29
7
∑
i=1
62
= ⋅ + ⋅ 62 = ⋅ 1953 + ⋅ 62
−11
2
62 ⋅ (62 + 1)
2
29
7
−11
2
29
7
= + =
−21483
2
1798
7
−146785
14
( i − 2)∑
i=1
97 11
2
= i − 2 = i − 2 1 = ⋅ − 2 ⋅ 97∑
i=1
97 11
2
∑
i=1
97 11
2
∑
i=1
97
∑
i=1
97 11
2
97 ⋅ (97 + 1)
2
= ⋅ 4753 − 2 ⋅ 97 = − 194 =
11
2
52283
2
51895
2
( i + )∑
i=1
90 −3
10
6
5
= i + = i + 1∑
i=1
90 −3
10
∑
i=1
90 6
5
−3
10
∑
i=1
90 6
5
∑
i=1
90
= ⋅ + ⋅ 90 = ⋅ 4095 + ⋅ 90
−3
10
90 ⋅ (90 + 1)
2
6
5
−3
10
6
5
= + 108 =
−2457
2
−2241
2
( i + )∑
i=1
66 −45
2
17
5
= i + = i + 1∑
i=1
66 −45
2
∑
i=1
66 17
5
−45
2
∑
i=1
66 17
5
∑
i=1
66
= ⋅ + ⋅ 66 = ⋅ 2211 + ⋅ 66
−45
2
66 ⋅ (66 + 1)
2
17
5
−45
2
17
5
= + =
−99495
2
1122
5
−495231
10
( i + )∑
i=1
74
−5
2
16
5
= i + = i + 1∑
i=1
74
−5
2
∑
i=1
74 16
5
−5
2
∑
i=1
74 16
5
∑
i=1
74
= ⋅ + ⋅ 74 = ⋅ 2775 + ⋅ 74
−5
2
74 ⋅ (74 + 1)
2
16
5
−5
2
16
5
= + =
−13875
2
1184
5
−67007
10
( i − 2)∑
i=1
83 −37
7
= i − 2 = i − 2 1 = ⋅ − 2 ⋅ 83∑
i=1
83 −37
7
∑
i=1
83 −37
7
∑
i=1
83
∑
i=1
83 −37
7
83 ⋅ (83 + 1)
2
= ⋅ 3486 − 2 ⋅ 83 = −18426 − 166 = −18592
−37
7
58).
59).
60).
61).
62).
63).
64).
65).
( i − )∑
i=1
90 1
2
7
2
= i − = i − 1∑
i=1
90 1
2
∑
i=1
90 7
2
1
2
∑
i=1
90 7
2
∑
i=1
90
= ⋅ − ⋅ 90 = ⋅ 4095 − ⋅ 90
1
2
90 ⋅ (90 + 1)
2
7
2
1
2
7
2
= − 315 =
4095
2
3465
2
( i − )∑
i=1
64 −25
4
31
5
= i − = i − 1∑
i=1
64 −25
4
∑
i=1
64 31
5
−25
4
∑
i=1
64 31
5
∑
i=1
64
= ⋅ − ⋅ 64 = ⋅ 2080 − ⋅ 64
−25
4
64 ⋅ (64 + 1)
2
31
5
−25
4
31
5
= −13000 − =
1984
5
−66984
5
( i − )∑
i=1
51 −16
3
3
10
= i − = i − 1∑
i=1
51 −16
3
∑
i=1
51 3
10
−16
3
∑
i=1
51 3
10
∑
i=1
51
= ⋅ − ⋅ 51 = ⋅ 1326 − ⋅ 51
−16
3
51 ⋅ (51 + 1)
2
3
10
−16
3
3
10
= −7072 − =
153
10
−70873
10
( i − 3)∑
i=1
78
−31
9
= i − 3 = i − 3 1 = ⋅ − 3 ⋅ 78∑
i=1
78
−31
9
∑
i=1
78
−31
9
∑
i=1
78
∑
i=1
78
−31
9
78 ⋅ (78 + 1)
2
= ⋅ 3081 − 3 ⋅ 78 = − 234 =
−31
9
−31837
3
−32539
3
( i + )∑
i=1
60 5
3
5
3
= i + = i + 1∑
i=1
60 5
3
∑
i=1
60 5
3
5
3
∑
i=1
60 5
3
∑
i=1
60
= ⋅ + ⋅ 60 = ⋅ 1830 + ⋅ 60
5
3
60 ⋅ (60 + 1)
2
5
3
5
3
5
3
= 3050 + 100 = 3150
( i − 4)∑
i=1
66
−15
7
= i − 4 = i − 4 1 = ⋅ − 4 ⋅ 66∑
i=1
66
−15
7
∑
i=1
66
−15
7
∑
i=1
66
∑
i=1
66
−15
7
66 ⋅ (66 + 1)
2
= ⋅ 2211 − 4 ⋅ 66 = − 264 =
−15
7
−33165
7
−35013
7
(−6i − )∑
i=1
93 5
8
= −6i − = −6 i − 1 = −6 ⋅ − ⋅ 93∑
i=1
93
∑
i=1
93 5
8
∑
i=1
93 5
8
∑
i=1
93 93 ⋅ (93 + 1)
2
5
8
= −6 ⋅ 4371 − ⋅ 93 = −26226 − =
5
8
465
8
−210273
8
( i − 9)∑
i=1
61 −25
7
= i − 9 = i − 9 1 = ⋅ − 9 ⋅ 61∑
i=1
61 −25
7
∑
i=1
61 −25
7
∑
i=1
61
∑
i=1
61 −25
7
61 ⋅ (61 + 1)
2
= ⋅ 1891 − 9 ⋅ 61 = − 549 =
−25
7
−47275
7
−51118
7
66).
67).
68).
69).
70).
71).
72).
73).
(6i + )∑
i=1
69 17
4
= 6i + = 6 i + 1 = 6 ⋅ + ⋅ 69∑
i=1
69
∑
i=1
69 17
4
∑
i=1
69 17
4
∑
i=1
69 69 ⋅ (69 + 1)
2
17
4
= 6 ⋅ 2415 + ⋅ 69 = 14490 + =
17
4
1173
4
59133
4
−7i = −7 i = −7 ⋅ = −7 ⋅ 2016 = −14112∑
i=1
63
∑
i=1
63 63 ⋅ (63 + 1)
2
( i − )∑
i=1
76 35
3
17
7
= i − = i − 1∑
i=1
76 35
3
∑
i=1
76 17
7
35
3
∑
i=1
76 17
7
∑
i=1
76
= ⋅ − ⋅ 76 = ⋅ 2926 − ⋅ 76
35
3
76 ⋅ (76 + 1)
2
17
7
35
3
17
7
= − =
102410
3
1292
7
712994
21
(−7i + )∑
i=1
67 3
2
= −7i + = −7 i + 1 = −7 ⋅ + ⋅ 67∑
i=1
67
∑
i=1
67 3
2
∑
i=1
67 3
2
∑
i=1
67 67 ⋅ (67 + 1)
2
3
2
= −7 ⋅ 2278 + ⋅ 67 = −15946 + =
3
2
201
2
−31691
2
( i − )∑
i=1
81
−23
4
47
10
= i − = i − 1∑
i=1
81
−23
4
∑
i=1
81 47
10
−23
4
∑
i=1
81 47
10
∑
i=1
81
= ⋅ − ⋅ 81 = ⋅ 3321 − ⋅ 81
−23
4
81 ⋅ (81 + 1)
2
47
10
−23
4
47
10
= − =
−76383
4
3807
10
−389529
20
( i − 9)∑
i=1
100 −1
2
= i − 9 = i − 9 1 = ⋅ − 9 ⋅ 100∑
i=1
100 −1
2
∑
i=1
100 −1
2
∑
i=1
100
∑
i=1
100 −1
2
100 ⋅ (100 + 1)
2
= ⋅ 5050 − 9 ⋅ 100 = −2525 − 900 = −3425
−1
2
( i + )∑
i=1
76 49
2
9
7
= i + = i + 1∑
i=1
76 49
2
∑
i=1
76 9
7
49
2
∑
i=1
76 9
7
∑
i=1
76
= ⋅ + ⋅ 76 = ⋅ 2926 + ⋅ 76
49
2
76 ⋅ (76 + 1)
2
9
7
49
2
9
7
= 71687 + =
684
7
502493
7
( i − )∑
i=1
70 1
10
40
9
= i − = i − 1∑
i=1
70 1
10
∑
i=1
70 40
9
1
10
∑
i=1
70 40
9
∑
i=1
70
= ⋅ − ⋅ 70 = ⋅ 2485 − ⋅ 70
1
10
70 ⋅ (70 + 1)
2
40
9
1
10
40
9
= − =
497
2
2800
9
−1127
18
74).
75).
76).
77).
78).
79).
80).
( i − )∑
i=1
57 −24
7
11
6
= i − = i − 1∑
i=1
57 −24
7
∑
i=1
57 11
6
−24
7
∑
i=1
57 11
6
∑
i=1
57
= ⋅ − ⋅ 57 = ⋅ 1653 − ⋅ 57
−24
7
57 ⋅ (57 + 1)
2
11
6
−24
7
11
6
= − =
−39672
7
209
2
−80807
14
(−4i − )∑
i=1
51 1
5
= −4i − = −4 i − 1 = −4 ⋅ − ⋅ 51∑
i=1
51
∑
i=1
51 1
5
∑
i=1
51 1
5
∑
i=1
51 51 ⋅ (51 + 1)
2
1
5
= −4 ⋅ 1326 − ⋅ 51 = −5304 − =
1
5
51
5
−26571
5
( i − 3)∑
i=1
95 27
5
= i − 3 = i − 3 1 = ⋅ − 3 ⋅ 95∑
i=1
95 27
5
∑
i=1
95 27
5
∑
i=1
95
∑
i=1
95 27
5
95 ⋅ (95 + 1)
2
= ⋅ 4560 − 3 ⋅ 95 = 24624 − 285 = 24339
27
5
( i − )∑
i=1
86 11
3
17
5
= i − = i − 1∑
i=1
86 11
3
∑
i=1
86 17
5
11
3
∑
i=1
86 17
5
∑
i=1
86
= ⋅ − ⋅ 86 = ⋅ 3741 − ⋅ 86
11
3
86 ⋅ (86 + 1)
2
17
5
11
3
17
5
= 13717 − =
1462
5
67123
5
( i + )∑
i=1
72 −9
5
11
4
= i + = i + 1∑
i=1
72 −9
5
∑
i=1
72 11
4
−9
5
∑
i=1
72 11
4
∑
i=1
72
= ⋅ + ⋅ 72 = ⋅ 2628 + ⋅ 72
−9
5
72 ⋅ (72 + 1)
2
11
4
−9
5
11
4
= + 198 =
−23652
5
−22662
5
(5i − )∑
i=1
73 31
2
= 5i − = 5 i − 1 = 5 ⋅ − ⋅ 73∑
i=1
73
∑
i=1
73 31
2
∑
i=1
73 31
2
∑
i=1
73 73 ⋅ (73 + 1)
2
31
2
= 5 ⋅ 2701 − ⋅ 73 = 13505 − =
31
2
2263
2
24747
2
( i − )∑
i=1
91 23
5
25
9
= i − = i − 1∑
i=1
91 23
5
∑
i=1
91 25
9
23
5
∑
i=1
91 25
9
∑
i=1
91
= ⋅ − ⋅ 91 = ⋅ 4186 − ⋅ 91
23
5
91 ⋅ (91 + 1)
2
25
9
23
5
25
9
= − =
96278
5
2275
9
855127
45
81).
82).
83).
84).
85).
86).
87).
(−2i − )∑
i=1
9645
7
= −2i − = −2 i − 1 = −2 ⋅ − ⋅ 96∑
i=1
96
∑
i=1
96 45
7
∑
i=1
96 45
7
∑
i=1
96 96 ⋅ (96 + 1)
2
45
7
= −2 ⋅ 4656 − ⋅ 96 = −9312 − =
45
7
4320
7
−69504
7
( i − )∑
i=1
82
−31
5
31
4
= i − = i − 1∑
i=1
82
−31
5
∑
i=1
82 31
4
−31
5
∑
i=1
82 31
4
∑
i=1
82
= ⋅ − ⋅ 82 = ⋅ 3403 − ⋅ 82
−31
5
82 ⋅ (82 + 1)
2
31
4
−31
5
31
4
= − =
−105493
5
1271
2
−217341
10
( i + )∑
i=1
91 45
8
13
5
= i + = i + 1∑
i=1
91 45
8
∑
i=1
91 13
5
45
8
∑
i=1
91 13
5
∑
i=1
91
= ⋅ + ⋅ 91 = ⋅ 4186 + ⋅ 91
45
8
91 ⋅ (91 + 1)
2
13
5
45
8
13
5
= + =
94185
4
1183
5
475657
20
( i − 2)∑
i=1
79 −9
4
= i − 2 = i − 2 1 = ⋅ − 2 ⋅ 79∑
i=1
79 −9
4
∑
i=1
79 −9
4
∑
i=1
79
∑
i=1
79 −9
4
79 ⋅ (79 + 1)
2
= ⋅ 3160 − 2 ⋅ 79 = −7110 − 158 = −7268
−9
4
( i − )∑
i=1
77 44
3
15
7
= i − = i − 1∑
i=1
77 44
3
∑
i=1
77 15
7
44
3
∑
i=1
77 15
7
∑
i=1
77
= ⋅ − ⋅ 77 = ⋅ 3003 − ⋅ 77
44
3
77 ⋅ (77 + 1)
2
15
7
44
3
15
7
= 44044 − 165 = 43879
( i − )∑
i=1
57 7
3
24
5
= i − = i − 1∑
i=1
57 7
3
∑
i=1
57 24
5
7
3
∑
i=1
57 24
5
∑
i=1
57
= ⋅ − ⋅ 57 = ⋅ 1653 − ⋅ 57
7
3
57 ⋅ (57 + 1)
2
24
5
7
3
24
5
= 3857 − =
1368
5
17917
5
( i − )∑
i=1
88 −12
5
2
3
= i − = i − 1∑
i=1
88 −12
5
∑
i=1
88 2
3
−12
5
∑
i=1
88 2
3
∑
i=1
88
= ⋅ − ⋅ 88 = ⋅ 3916 − ⋅ 88
−12
5
88 ⋅ (88 + 1)
2
2
3
−12
5
2
3
= − =
−46992
5
176
3
−141856
15
88).
89).
90).
91).
92).
93).
94).
( i + 8)∑
i=1
69 −17
10
= i + 8 = i + 8 1 = ⋅ + 8 ⋅ 69∑
i=1
69 −17
10
∑
i=1
69 −17
10
∑
i=1
69
∑
i=1
69 −17
10
69 ⋅ (69 + 1)
2
= ⋅ 2415 + 8 ⋅ 69 = + 552 =
−17
10
−8211
2
−7107
2
( i − )∑
i=1
56 45
4
37
5
= i − = i − 1∑
i=1
56 45
4
∑
i=1
56 37
5
45
4
∑
i=1
56 37
5
∑
i=1
56
= ⋅ − ⋅ 56 = ⋅ 1596 − ⋅ 56
45
4
56 ⋅ (56 + 1)
2
37
5
45
4
37
5
= 17955 − =
2072
5
87703
5
( i − 23)∑
i=1
97 −2
3
= i − 23 = i − 23 1 = ⋅ − 23 ⋅ 97∑
i=1
97 −2
3
∑
i=1
97 −2
3
∑
i=1
97
∑
i=1
97 −2
3
97 ⋅ (97 + 1)
2
= ⋅ 4753 − 23 ⋅ 97 = − 2231 =
−2
3
−9506
3
−16199
3
( i − )∑
i=1
79 25
7
37
6
= i − = i − 1∑
i=1
79 25
7
∑
i=1
79 37
6
25
7
∑
i=1
79 37
6
∑
i=1
79
= ⋅ − ⋅ 79 = ⋅ 3160 − ⋅ 79
25
7
79 ⋅ (79 + 1)
2
37
6
25
7
37
6
= − =
79000
7
2923
6
453539
42
( i − )∑
i=1
51 22
3
1
2
= i − = i − 1∑
i=1
51 22
3
∑
i=1
51 1
2
22
3
∑
i=1
51 1
2
∑
i=1
51
= ⋅ − ⋅ 51 = ⋅ 1326 − ⋅ 51
22
3
51 ⋅ (51 + 1)
2
1
2
22
3
1
2
= 9724 − =
51
2
19397
2
( i + )∑
i=1
95 13
8
9
2
= i + = i + 1∑
i=1
95 13
8
∑
i=1
95 9
2
13
8
∑
i=1
95 9
2
∑
i=1
95
= ⋅ + ⋅ 95 = ⋅ 4560 + ⋅ 95
13
8
95 ⋅ (95 + 1)
2
9
2
13
8
9
2
= 7410 + =
855
2
15675
2
(−3i − )∑
i=1
65 1
5
= −3i − = −3 i − 1 = −3 ⋅ − ⋅ 65∑
i=1
65
∑
i=1
65 1
5
∑
i=1
65 1
5
∑
i=1
65 65 ⋅ (65 + 1)
2
1
5
= −3 ⋅ 2145 − ⋅ 65 = −6435 − 13 = −6448
1
5
95).
96).
97).
98).
99).
100).
101).
( i − )∑
i=1
67 29
6
2
5
= i − = i − 1∑
i=1
67 29
6
∑
i=1
67 2
5
29
6
∑
i=1
67 2
5
∑
i=1
67
= ⋅ − ⋅ 67 = ⋅ 2278 − ⋅ 67
29
6
67 ⋅ (67 + 1)
2
2
5
29
6
2
5
= − =
33031
3
134
5
164753
15
( i + )∑
i=1
78 −22
3
44
7
= i + = i + 1∑
i=1
78 −22
3
∑
i=1
78 44
7
−22
3
∑
i=1
78 44
7
∑
i=1
78
= ⋅ + ⋅ 78 = ⋅ 3081 + ⋅ 78
−22
3
78 ⋅ (78 + 1)
2
44
7
−22
3
44
7
= −22594 + =
3432
7
−154726
7
( i − )∑
i=1
72
−24
7
43
8
= i − = i − 1∑
i=1
72
−24
7
∑
i=1
72 43
8
−24
7
∑
i=1
72 43
8
∑
i=1
72
= ⋅ − ⋅ 72 = ⋅ 2628 − ⋅ 72
−24
7
72 ⋅ (72 + 1)
2
43
8
−24
7
43
8
= − 387 =
−63072
7
−65781
7
( i + )∑
i=1
79 47
7
5
2
= i + = i + 1∑
i=1
79 47
7
∑
i=1
79 5
2
47
7
∑
i=1
79 5
2
∑
i=1
79
= ⋅ + ⋅ 79 = ⋅ 3160 + ⋅ 79
47
7
79 ⋅ (79 + 1)
2
5
2
47
7
5
2
= + =
148520
7
395
2
299805
14
(−4i + )∑
i=1
51 37
7
= −4i + = −4 i + 1 = −4 ⋅ + ⋅ 51∑
i=1
51
∑
i=1
51 37
7
∑
i=1
51 37
7
∑
i=1
51 51 ⋅ (51 + 1)
2
37
7
= −4 ⋅ 1326 + ⋅ 51 = −5304 + =
37
7
1887
7
−35241
7
(4i − )∑
i=1
93 25
9
= 4i − = 4 i − 1 = 4 ⋅ − ⋅ 93∑
i=1
93
∑
i=1
93 25
9
∑
i=1
93 25
9
∑
i=1
93 93 ⋅ (93 + 1)
2
25
9
= 4 ⋅ 4371 − ⋅ 93 = 17484 − =
25
9
775
3
51677
3
( i − )∑
i=1
100 4
5
25
9
= i − = i − 1∑
i=1
100 4
5
∑
i=1
100 25
9
4
5
∑
i=1
100 25
9
∑
i=1
100
= ⋅ − ⋅ 100 = ⋅ 5050 − ⋅ 100
4
5
100 ⋅ (100 + 1)
2
25
9
4
5
25
9
= 4040 − =
2500
9
33860
9
102).
103).
104).
105).
106).
107).
108).
( i + )∑
i=1
64 27
7
50
3
= i + = i + 1∑
i=1
64 27
7
∑
i=1
64 50
3
27
7
∑
i=1
64 50
3
∑
i=1
64
= ⋅ + ⋅ 64 = ⋅ 2080 + ⋅ 64
27
7
64 ⋅ (64 + 1)
2
50
3
27
7
50
3
= + =
56160
7
3200
3
190880
21
( i + )∑
i=1
97 −47
4
13
3
= i + = i + 1∑
i=1
97 −47
4
∑
i=1
97 13
3
−47
4
∑
i=1
97 13
3
∑
i=1
97
= ⋅ + ⋅ 97 = ⋅ 4753 + ⋅ 97
−47
4
97 ⋅ (97 + 1)
2
13
3
−47
4
13
3
= + =
−223391
4
1261
3
−665129
12
( i − )∑
i=1
77 11
9
9
10
= i − = i − 1∑
i=1
77 11
9
∑
i=1
77 9
10
11
9
∑
i=1
77 9
10
∑
i=1
77
= ⋅ − ⋅ 77 = ⋅ 3003 − ⋅ 77
11
9
77 ⋅ (77 + 1)
2
9
10
11
9
9
10
= − =
11011
3
693
10
108031
30
(−24i − )∑
i=1
90 14
5
= −24i − = −24 i − 1 = −24 ⋅ − ⋅ 90∑
i=1
90
∑
i=1
90 14
5
∑
i=1
90 14
5
∑
i=1
90 90 ⋅ (90 + 1)
2
14
5
= −24 ⋅ 4095 − ⋅ 90 = −98280 − 252 = −98532
14
5
( i − )∑
i=1
72 19
9
46
5
= i − = i − 1∑
i=1
72 19
9
∑
i=1
72 46
5
19
9
∑
i=1
72 46
5
∑
i=1
72
= ⋅ − ⋅ 72 = ⋅ 2628 − ⋅ 72
19
9
72 ⋅ (72 + 1)
2
46
5
19
9
46
5
= 5548 − =
3312
5
24428
5
(−2i + )∑
i=1
88 43
4
= −2i + = −2 i + 1 = −2 ⋅ + ⋅ 88∑
i=1
88
∑
i=1
88 43
4
∑
i=1
88 43
4
∑
i=1
88 88 ⋅ (88 + 1)
2
43
4
= −2 ⋅ 3916 + ⋅ 88 = −7832 + 946 = −6886
43
4
( i + )∑
i=1
58 18
5
26
9
= i + = i + 1∑
i=1
58 18
5
∑
i=1
58 26
9
18
5
∑
i=1
58 26
9
∑
i=1
58
= ⋅ + ⋅ 58 = ⋅ 1711 + ⋅ 58
18
5
58 ⋅ (58 + 1)
2
26
9
18
5
26
9
= + =
30798
5
1508
9
284722
45
109).
110).
111).
112).
113).
114).
115).
(−4i + )∑
i=1
56 10
7
= −4i + = −4 i + 1 = −4 ⋅ + ⋅ 56∑
i=1
56
∑
i=1
56 10
7
∑
i=1
56 10
7
∑
i=1
56 56 ⋅ (56 + 1)
2
10
7
= −4 ⋅ 1596 + ⋅ 56 = −6384 + 80 = −6304
10
7
(−20i − )∑
i=1
62 13
3
= −20i − = −20 i − 1 = −20 ⋅ − ⋅ 62∑
i=1
62
∑
i=1
62 13
3
∑
i=1
62 13
3
∑
i=1
62 62 ⋅ (62 + 1)
2
13
3
= −20 ⋅ 1953 − ⋅ 62 = −39060 − =
13
3
806
3
−117986
3
( i + )∑
i=1
88 28
5
25
7
= i + = i + 1∑
i=1
88 28
5
∑
i=1
88 25
7
28
5
∑
i=1
88 25
7
∑
i=1
88
= ⋅ + ⋅ 88 = ⋅ 3916 + ⋅ 88
28
5
88 ⋅ (88 + 1)
2
25
7
28
5
25
7
= + =
109648
5
2200
7
778536
35
( i − )∑
i=1
52 5
2
10
7
= i − = i − 1∑
i=1
52 5
2
∑
i=1
52 10
7
5
2
∑
i=1
52 10
7
∑
i=1
52
= ⋅ − ⋅ 52 = ⋅ 1378 − ⋅ 52
5
2
52 ⋅ (52 + 1)
2
10
7
5
2
10
7
= 3445 − =
520
7
23595
7
( i − )∑
i=1
74 46
7
14
5
= i − = i − 1∑
i=1
74 46
7
∑
i=1
74 14
5
46
7
∑
i=1
74 14
5
∑
i=1
74
= ⋅ − ⋅ 74 = ⋅ 2775 − ⋅ 74
46
7
74 ⋅ (74 + 1)
2
14
5
46
7
14
5
= − =
127650
7
1036
5
630998
35
( i + 4)∑
i=1
78
−8
7
= i + 4 = i + 4 1 = ⋅ + 4 ⋅ 78∑
i=1
78
−8
7
∑
i=1
78
−8
7
∑
i=1
78
∑
i=1
78
−8
7
78 ⋅ (78 + 1)
2
= ⋅ 3081 + 4 ⋅ 78 = + 312 =
−8
7
−24648
7
−22464
7
( i + 1)∑
i=1
70
−3
5
= i + 1 = i + 1 = ⋅ + 70∑
i=1
70
−3
5
∑
i=1
70
−3
5
∑
i=1
70
∑
i=1
70
−3
5
70 ⋅ (70 + 1)
2
= ⋅ 2485 + 70 = −1491 + 70 = −1421
−3
5
116).
117).
118).
119).
120).
121).
122).
( i − )∑
i=1
87 −3
5
49
9
= i − = i − 1∑
i=1
87 −3
5
∑
i=1
87 49
9
−3
5
∑
i=1
87 49
9
∑
i=1
87
= ⋅ − ⋅ 87 = ⋅ 3828 − ⋅ 87
−3
5
87 ⋅ (87 + 1)
2
49
9
−3
5
49
9
= − =
−11484
5
1421
3
−41557
15
( i − )∑
i=1
69 −37
10
17
10
= i − = i − 1∑
i=1
69 −37
10
∑
i=1
69 17
10
−37
10
∑
i=1
69 17
10
∑
i=1
69
= ⋅ − ⋅ 69 = ⋅ 2415 − ⋅ 69
−37
10
69 ⋅ (69 + 1)
2
17
10
−37
10
17
10
= − =
−17871
2
1173
10
−45264
5
( i − 5)∑
i=1
87
−17
2
= i − 5 = i − 5 1 = ⋅ − 5 ⋅ 87∑
i=1
87
−17
2
∑
i=1
87
−17
2
∑
i=1
87
∑
i=1
87
−17
2
87 ⋅ (87 + 1)
2
= ⋅ 3828 − 5 ⋅ 87 = −32538− 435 = −32973
−17
2
( i − )∑
i=1
101 −7
5
16
7
= i − = i − 1∑
i=1
101 −7
5
∑
i=1
101 16
7
−7
5
∑
i=1
101 16
7
∑
i=1
101
= ⋅ − ⋅ 101 = ⋅ 5151 − ⋅ 101
−7
5
101 ⋅ (101 + 1)
2
16
7
−7
5
16
7
= − =
−36057
5
1616
7
−260479
35
( i + )∑
i=1
69 17
5
31
9
= i + = i + 1∑
i=1
69 17
5
∑
i=1
69 31
9
17
5
∑
i=1
69 31
9
∑
i=1
69
= ⋅ + ⋅ 69 = ⋅ 2415 + ⋅ 69
17
5
69 ⋅ (69 + 1)
2
31
9
17
5
31
9
= 8211 + =
713
3
25346
3
(3i + )∑
i=1
99 47
3
= 3i + = 3 i + 1 = 3 ⋅ + ⋅ 99∑
i=1
99
∑
i=1
99 47
3
∑
i=1
99 47
3
∑
i=1
99 99 ⋅ (99 + 1)
2
47
3
= 3 ⋅ 4950 + ⋅ 99 = 14850 + 1551 = 16401
47
3
(−8i + )∑
i=1
59 18
5
= −8i + = −8 i + 1 = −8 ⋅ + ⋅ 59∑
i=1
59
∑
i=1
59 18
5
∑
i=1
59 18
5
∑
i=1
59 59 ⋅ (59 + 1)
2
18
5
= −8 ⋅ 1770 + ⋅ 59 = −14160 + =
18
5
1062
5
−69738
5
123).
124).
125).
126).
127).
128).
129).
130).
(−8i + )∑
i=1
99 19
6
= −8i + = −8 i + 1 = −8 ⋅ + ⋅ 99∑
i=1
99
∑
i=1
99 19
6
∑
i=1
99 19
6
∑
i=1
99 99 ⋅ (99 + 1)
2
19
6
= −8 ⋅ 4950 + ⋅ 99 = −39600 + =
19
6
627
2
−78573
2
(12i + 3)∑
i=1
83
= 12i + 3 = 12 i + 3 1 = 12 ⋅ + 3 ⋅ 83∑
i=1
83
∑
i=1
83
∑
i=1
83
∑
i=1
83 83 ⋅ (83 + 1)
2
= 12 ⋅ 3486 + 3 ⋅ 83 = 41832 + 249 = 42081
( i − 2)∑
i=1
56 23
4
= i − 2 = i − 2 1 = ⋅ − 2 ⋅ 56∑
i=1
56 23
4
∑
i=1
56 23
4
∑
i=1
56
∑
i=1
56 23
4
56 ⋅ (56 + 1)
2
= ⋅ 1596 − 2 ⋅ 56 = 9177 − 112 = 9065
23
4
( i − )∑
i=1
80 −47
5
13
2
= i − = i − 1∑
i=1
80 −47
5
∑
i=1
80 13
2
−47
5
∑
i=1
80 13
2
∑
i=1
80
= ⋅ − ⋅ 80 = ⋅ 3240 − ⋅ 80
−47
5
80 ⋅ (80 + 1)
2
13
2
−47
5
13
2
= −30456 − 520 = −30976
( i − )∑
i=1
54 −17
4
23
8
= i − = i − 1∑
i=1
54 −17
4
∑
i=1
54 23
8
−17
4
∑
i=1
54 23
8
∑
i=1
54
= ⋅ − ⋅ 54 = ⋅ 1485 − ⋅ 54
−17
4
54 ⋅ (54 + 1)
2
23
8
−17
4
23
8
= − =
−25245
4
621
4
−12933
2
( i − )∑
i=1
91 4
7
1
3
= i − = i − 1∑
i=1
91 4
7
∑
i=1
91 1
3
4
7
∑
i=1
91 1
3
∑
i=1
91
= ⋅ − ⋅ 91 = ⋅ 4186 − ⋅ 91
4
7
91 ⋅ (91 + 1)
2
1
3
4
7
1
3
= 2392 − =
91
3
7085
3
(6i − 22)∑
i=1
76
= 6i − 22 = 6 i − 22 1 = 6 ⋅ − 22 ⋅ 76∑
i=1
76
∑
i=1
76
∑
i=1
76
∑
i=1
76 76 ⋅ (76 + 1)
2
= 6 ⋅ 2926 − 22 ⋅ 76 = 17556 − 1672 = 15884
( i + 6)∑
i=1
87 −9
5
= i + 6 = i + 6 1 = ⋅ + 6 ⋅ 87∑
i=1
87 −9
5
∑
i=1
87 −9
5
∑
i=1
87
∑
i=1
87 −9
5
87 ⋅ (87 + 1)
2
= ⋅ 3828 + 6 ⋅ 87 = + 522 =
−9
5
−34452
5
−31842
5
131).
132).
133).
134).
135).
136).
137).
138).
( i − 10)∑
i=1
98 1
7
= i − 10 = i − 10 1 = ⋅ − 10 ⋅ 98∑
i=1
98 1
7
∑
i=1
98 1
7
∑
i=1
98
∑
i=1
98 1
7
98 ⋅ (98 + 1)
2
= ⋅ 4851 − 10 ⋅ 98 = 693 − 980 = −287
1
7
(−7i + 10)∑
i=1
90
= −7i + 10 = −7 i + 10 1 = −7 ⋅ + 10 ⋅ 90∑
i=1
90
∑
i=1
90
∑
i=1
90
∑
i=1
90 90 ⋅ (90 + 1)
2
= −7 ⋅ 4095 + 10 ⋅ 90 = −28665 + 900 = −27765
( i − 1)∑
i=1
98 −12
5
= i − 1 = i − 1 = ⋅ − 98∑
i=1
98 −12
5
∑
i=1
98 −12
5
∑
i=1
98
∑
i=1
98 −12
5
98 ⋅ (98 + 1)
2
= ⋅ 4851 − 98 = − 98 =
−12
5
−58212
5
−58702
5
( i + 3)∑
i=1
98 29
7
= i + 3 = i + 3 1 = ⋅ + 3 ⋅ 98∑
i=1
98 29
7
∑
i=1
98 29
7
∑
i=1
98
∑
i=1
98 29
7
98 ⋅ (98 + 1)
2
= ⋅ 4851 + 3 ⋅ 98 = 20097 + 294 = 20391
29
7
( i − )∑
i=1
50 −43
10
5
2
= i − = i − 1∑
i=1
50 −43
10
∑
i=1
50 5
2
−43
10
∑
i=1
50 5
2
∑
i=1
50
= ⋅ − ⋅ 50 = ⋅ 1275 − ⋅ 50
−43
10
50 ⋅ (50 + 1)
2
5
2
−43
10
5
2
= − 125 =
−10965
2
−11215
2
( i − )∑
i=1
62 26
7
8
3
= i − = i − 1∑
i=1
62 26
7
∑
i=1
62 8
3
26
7
∑
i=1
62 8
3
∑
i=1
62
= ⋅ − ⋅ 62 = ⋅ 1953 − ⋅ 62
26
7
62 ⋅ (62 + 1)
2
8
3
26
7
8
3
= 7254 − =
496
3
21266
3
(9i + )∑
i=1
96 7
2
= 9i + = 9 i + 1 = 9 ⋅ + ⋅ 96∑
i=1
96
∑
i=1
96 7
2
∑
i=1
96 7
2
∑
i=1
96 96 ⋅ (96 + 1)
2
7
2
= 9 ⋅ 4656 + ⋅ 96 = 41904 + 336 = 42240
7
2
( i + )∑
i=1
90 1
3
4
3
= i + = i + 1∑
i=1
90 1
3
∑
i=1
90 4
3
1
3
∑
i=1
90 4
3
∑
i=1
90
= ⋅ + ⋅ 90 = ⋅ 4095 + ⋅ 90
1
3
90 ⋅ (90 + 1)
2
4
3
1
3
4
3
= 1365 + 120 = 1485
139).
140).
141).
142).
143).
144).
145).
(−15i + )∑
i=1
85 41
9
= −15i + = −15 i + 1 = −15 ⋅ + ⋅ 85∑
i=1
85
∑
i=1
85 41
9
∑
i=1
85 41
9
∑
i=1
85 85 ⋅ (85 + 1)
2
41
9
= −15 ⋅ 3655 + ⋅ 85 = −54825 + =
41
9
3485
9
−489940
9
( i + )∑
i=1
51 49
10
23
3
= i + = i + 1∑
i=1
51 49
10
∑
i=1
51 23
3
49
10
∑
i=1
51 23
3
∑
i=1
51
= ⋅ + ⋅ 51 = ⋅ 1326 + ⋅ 51
49
10
51 ⋅ (51 + 1)
2
23
3
49
10
23
3
= + 391 =
32487
5
34442
5
( i − )∑
i=1
88 −16
9
45
7
= i − = i − 1∑
i=1
88 −16
9
∑
i=1
88 45
7
−16
9
∑
i=1
88 45
7
∑
i=1
88
= ⋅ − ⋅ 88 = ⋅ 3916 − ⋅ 88
−16
9
88 ⋅ (88 + 1)
2
45
7
−16
9
45
7
= − =
−62656
9
3960
7
−474232
63
( i + )∑
i=1
68 −25
3
7
2
= i + = i + 1∑
i=1
68 −25
3
∑
i=1
68 7
2
−25
3
∑
i=1
68 7
2
∑
i=1
68
= ⋅ + ⋅ 68 = ⋅ 2346 + ⋅ 68
−25
3
68 ⋅ (68 + 1)
2
7
2
−25
3
7
2
= −19550 + 238 = −19312
( i + )∑
i=1
63 −29
8
23
6
= i + = i + 1∑
i=1
63 −29
8
∑
i=1
63 23
6
−29
8
∑
i=1
63 23
6
∑
i=1
63
= ⋅ + ⋅ 63 = ⋅ 2016 + ⋅ 63
−29
8
63 ⋅ (63 + 1)
2
23
6
−29
8
23
6
= −7308 + =
483
2
−14133
2
( i − )∑
i=1
50 16
3
11
4
= i − = i − 1∑
i=1
50 16
3
∑
i=1
50 11
4
16
3
∑
i=1
50 11
4
∑
i=1
50
= ⋅ − ⋅ 50 = ⋅ 1275 − ⋅ 50
16
3
50 ⋅ (50 + 1)
2
11
4
16
3
11
4
= 6800 − =
275
2
13325
2
( i + )∑
i=1
83
−3
2
41
6
= i + = i + 1∑
i=1
83
−3
2
∑
i=1
83 41
6
−3
2
∑
i=1
83 41
6
∑
i=1
83
= ⋅ + ⋅ 83 = ⋅ 3486 + ⋅ 83
−3
2
83 ⋅ (83 + 1)
2
41
6
−3
2
41
6
= −5229 + =
3403
6
−27971
6
146).
147).
148).
149).
150).
151).
152).
( i + 3)∑
i=1
94 −47
2
= i + 3 = i + 3 1 = ⋅ + 3 ⋅ 94∑
i=1
94 −47
2
∑
i=1
94 −47
2
∑
i=1
94
∑
i=1
94 −47
2
94 ⋅ (94 + 1)
2
= ⋅ 4465 + 3 ⋅ 94 = + 282 =
−47
2
−209855
2
−209291
2
(10i + )∑
i=1
73 1
2
= 10i + = 10 i + 1 = 10 ⋅ + ⋅ 73∑
i=1
73
∑
i=1
73 1
2
∑
i=1
73 1
2
∑
i=1
73 73 ⋅ (73 + 1)
2
1
2
= 10 ⋅ 2701 + ⋅ 73 = 27010 + =
1
2
73
2
54093
2
( i − )∑
i=1
80 42
5
41
8
= i − = i − 1∑
i=1
80 42
5
∑
i=1
80 41
8
42
5
∑
i=1
80 41
8
∑
i=1
80
= ⋅ − ⋅ 80 = ⋅ 3240 − ⋅ 80
42
5
80 ⋅ (80 + 1)
2
41
8
42
5
41
8
= 27216 − 410 = 26806
( i − )∑
i=1
95 11
7
39
5
= i − = i − 1∑
i=1
95 11
7
∑
i=1
95 39
5
11
7
∑
i=1
95 39
5
∑
i=1
95
= ⋅ − ⋅ 95 = ⋅ 4560 − ⋅ 95
11
7
95 ⋅ (95 + 1)
2
39
5
11
7
39
5
= − 741 =
50160
7
44973
7
( i + )∑
i=1
67 −1
3
11
4
= i + = i + 1∑
i=1
67 −1
3
∑
i=1
67 11
4
−1
3
∑
i=1
67 11
4
∑
i=1
67
= ⋅ + ⋅ 67 = ⋅ 2278 + ⋅ 67
−1
3
67 ⋅ (67 + 1)
2
11
4
−1
3
11
4
= + =
−2278
3
737
4
−6901
12
( i + )∑
i=1
91 −1
7
27
8
= i + = i + 1∑
i=1
91 −1
7
∑
i=1
91 27
8
−1
7
∑
i=1
91 27
8
∑
i=1
91
= ⋅ + ⋅ 91 = ⋅ 4186 + ⋅ 91
−1
7
91 ⋅ (91 + 1)
2
27
8
−1
7
27
8
= −598 + =
2457
8
−2327
8
( i + )∑
i=1
94 10
7
2
7
= i + = i + 1∑
i=1
94 10
7
∑
i=1
94 2
7
10
7
∑
i=1
94 2
7
∑
i=1
94
= ⋅ + ⋅ 94 = ⋅ 4465 + ⋅ 94
10
7
94 ⋅ (94 + 1)
2
2
7
10
7
2
7
= + =
44650
7
188
7
44838
7
153).
154).
155).
156).
157).
158).
( i − )∑
i=1
57 −38
5
39
7
= i − = i − 1∑
i=1
57 −38
5
∑
i=1
57 39
7
−38
5
∑
i=1
57 39
7
∑
i=1
57
= ⋅ − ⋅ 57 = ⋅ 1653 − ⋅ 57
−38
5
57 ⋅ (57 + 1)
2
39
7
−38
5
39
7
= − =
−62814
5
2223
7
−450813
35
( i − )∑
i=1
83 −43
7
17
7
= i − = i − 1∑
i=1
83 −43
7
∑
i=1
83 17
7
−43
7
∑
i=1
83 17
7
∑
i=1
83
= ⋅ − ⋅ 83 = ⋅ 3486 − ⋅ 83
−43
7
83 ⋅ (83 + 1)
2
17
7
−43
7
17
7
= −21414 − =
1411
7
−151309
7
( i − )∑
i=1
101 27
7
13
5
= i − = i − 1∑
i=1
101 27
7
∑
i=1
101 13
5
27
7
∑
i=1
101 13
5
∑
i=1
101
= ⋅ − ⋅ 101 = ⋅ 5151 − ⋅ 101
27
7
101 ⋅ (101 + 1)
2
13
5
27
7
13
5
= − =
139077
7
1313
5
686194
35
( i − )∑
i=1
88 27
7
1
2
= i − = i − 1∑
i=1
88 27
7
∑
i=1
88 1
2
27
7
∑
i=1
88 1
2
∑
i=1
88
= ⋅ − ⋅ 88 = ⋅ 3916 − ⋅ 88
27
7
88 ⋅ (88 + 1)
2
1
2
27
7
1
2
= − 44 =
105732
7
105424
7
( i − )∑
i=1
91 17
7
1
2
= i − = i − 1∑
i=1
91 17
7
∑
i=1
91 1
2
17
7
∑
i=1
911
2
∑
i=1
91
= ⋅ − ⋅ 91 = ⋅ 4186 − ⋅ 91
17
7
91 ⋅ (91 + 1)
2
1
2
17
7
1
2
= 10166 − =
91
2
20241
2
( i + )∑
i=1
55 17
5
14
3
= i + = i + 1∑
i=1
55 17
5
∑
i=1
55 14
3
17
5
∑
i=1
55 14
3
∑
i=1
55
= ⋅ + ⋅ 55 = ⋅ 1540 + ⋅ 55
17
5
55 ⋅ (55 + 1)
2
14
3
17
5
14
3
= 5236 + =
770
3
16478
3
159).
160).
161).
162).
163).
164).
165).
( i − )∑
i=1
55
−7
2
19
6
= i − = i − 1∑
i=1
55 −7
2
∑
i=1
55 19
6
−7
2
∑
i=1
55 19
6
∑
i=1
55
= ⋅ − ⋅ 55 = ⋅ 1540 − ⋅ 55
−7
2
55 ⋅ (55 + 1)
2
19
6
−7
2
19
6
= −5390 − =
1045
6
−33385
6
( i − )∑
i=1
50 32
7
31
3
= i − = i − 1∑
i=1
50 32
7
∑
i=1
50 31
3
32
7
∑
i=1
50 31
3
∑
i=1
50
= ⋅ − ⋅ 50 = ⋅ 1275 − ⋅ 50
32
7
50 ⋅ (50 + 1)
2
31
3
32
7
31
3
= − =
40800
7
1550
3
111550
21
( i + )∑
i=1
70 49
6
8
5
= i + = i + 1∑
i=1
70 49
6
∑
i=1
70 8
5
49
6
∑
i=1
70 8
5
∑
i=1
70
= ⋅ + ⋅ 70 = ⋅ 2485 + ⋅ 70
49
6
70 ⋅ (70 + 1)
2
8
5
49
6
8
5
= + 112 =
121765
6
122437
6
( i + )∑
i=1
96 1
4
3
7
= i + = i + 1∑
i=1
96 1
4
∑
i=1
96 3
7
1
4
∑
i=1
96 3
7
∑
i=1
96
= ⋅ + ⋅ 96 = ⋅ 4656 + ⋅ 96
1
4
96 ⋅ (96 + 1)
2
3
7
1
4
3
7
= 1164 + =
288
7
8436
7
(−8i + )∑
i=1
77 37
7
= −8i + = −8 i + 1 = −8 ⋅ + ⋅ 77∑
i=1
77
∑
i=1
77 37
7
∑
i=1
77 37
7
∑
i=1
77 77 ⋅ (77 + 1)
2
37
7
= −8 ⋅ 3003 + ⋅ 77 = −24024 + 407 = −23617
37
7
(−6i − )∑
i=1
79 23
7
= −6i − = −6 i − 1 = −6 ⋅ − ⋅ 79∑
i=1
79
∑
i=1
79 23
7
∑
i=1
79 23
7
∑
i=1
79 79 ⋅ (79 + 1)
2
23
7
= −6 ⋅ 3160 − ⋅ 79 = −18960 − =
23
7
1817
7
−134537
7
( i − 2)∑
i=1
88 8
5
= i − 2 = i − 2 1 = ⋅ − 2 ⋅ 88∑
i=1
88 8
5
∑
i=1
88 8
5
∑
i=1
88
∑
i=1
88 8
5
88 ⋅ (88 + 1)
2
= ⋅ 3916 − 2 ⋅ 88 = − 176 =
8
5
31328
5
30448
5
166).
167).
168).
169).
170).
171).
172).
( i + )∑
i=1
89 1
9
25
3
= i + = i + 1∑
i=1
89 1
9
∑
i=1
89 25
3
1
9
∑
i=1
89 25
3
∑
i=1
89
= ⋅ + ⋅ 89 = ⋅ 4005 + ⋅ 89
1
9
89 ⋅ (89 + 1)
2
25
3
1
9
25
3
= 445 + =
2225
3
3560
3
( i + 16)∑
i=1
51 −33
2
= i + 16 = i + 16 1 = ⋅ + 16 ⋅ 51∑
i=1
51 −33
2
∑
i=1
51 −33
2
∑
i=1
51
∑
i=1
51 −33
2
51 ⋅ (51 + 1)
2
= ⋅ 1326 + 16 ⋅ 51 = −21879 + 816 = −21063
−33
2
( i + )∑
i=1
86 −15
7
34
5
= i + = i + 1∑
i=1
86 −15
7
∑
i=1
86 34
5
−15
7
∑
i=1
86 34
5
∑
i=1
86
= ⋅ + ⋅ 86 = ⋅ 3741 + ⋅ 86
−15
7
86 ⋅ (86 + 1)
2
34
5
−15
7
34
5
= + =
−56115
7
2924
5
−260107
35
( i − )∑
i=1
68 22
5
39
4
= i − = i − 1∑
i=1
68 22
5
∑
i=1
68 39
4
22
5
∑
i=1
68 39
4
∑
i=1
68
= ⋅ − ⋅ 68 = ⋅ 2346 − ⋅ 68
22
5
68 ⋅ (68 + 1)
2
39
4
22
5
39
4
= − 663 =
51612
5
48297
5
( i − )∑
i=1
100
−23
5
25
3
= i − = i − 1∑
i=1
100
−23
5
∑
i=1
100 25
3
−23
5
∑
i=1
100 25
3
∑
i=1
100
= ⋅ − ⋅ 100 = ⋅ 5050 − ⋅ 100
−23
5
100 ⋅ (100 + 1)
2
25
3
−23
5
25
3
= −23230 − =
2500
3
−72190
3
( i + )∑
i=1
78 16
5
14
5
= i + = i + 1∑
i=1
78 16
5
∑
i=1
78 14
5
16
5
∑
i=1
78 14
5
∑
i=1
78
= ⋅ + ⋅ 78 = ⋅ 3081 + ⋅ 78
16
5
78 ⋅ (78 + 1)
2
14
5
16
5
14
5
= + =
49296
5
1092
5
50388
5
( i + )∑
i=1
66 −11
5
29
8
= i + = i + 1∑
i=1
66 −11
5
∑
i=1
66 29
8
−11
5
∑
i=1
66 29
8
∑
i=1
66
= ⋅ + ⋅ 66 = ⋅ 2211 + ⋅ 66
−11
5
66 ⋅ (66 + 1)
2
29
8
−11
5
29
8
= + =
−24321
5
957
4
−92499
20
173).
174).
175).
176).
177).
178).
179).
( i + )∑
i=1
58
−3
4
4
3
= i + = i + 1∑
i=1
58 −3
4
∑
i=1
58 4
3
−3
4
∑
i=1
58 4
3
∑
i=1
58
= ⋅ + ⋅ 58 = ⋅ 1711 + ⋅ 58
−3
4
58 ⋅ (58 + 1)
2
4
3
−3
4
4
3
= + =
−5133
4
232
3
−14471
12
( i + )∑
i=1
94 7
6
26
3
= i + = i + 1∑
i=1
94 7
6
∑
i=1
94 26
3
7
6
∑
i=1
94 26
3
∑
i=1
94
= ⋅ + ⋅ 94 = ⋅ 4465 + ⋅ 94
7
6
94 ⋅ (94 + 1)
2
26
3
7
6
26
3
= + =
31255
6
2444
3
36143
6
(7i − )∑
i=1
78 5
9
= 7i − = 7 i − 1 = 7 ⋅ − ⋅ 78∑
i=1
78
∑
i=1
78 5
9
∑
i=1
78 5
9
∑
i=1
78 78 ⋅ (78 + 1)
2
5
9
= 7 ⋅ 3081 − ⋅ 78 = 21567 − =
5
9
130
3
64571
3
( i + 17)∑
i=1
73 −13
3
= i + 17 = i + 17 1 = ⋅ + 17 ⋅ 73∑
i=1
73 −13
3
∑
i=1
73 −13
3
∑
i=1
73
∑
i=1
73 −13
3
73 ⋅ (73 + 1)
2
= ⋅ 2701 + 17 ⋅ 73 = + 1241 =
−13
3
−35113
3
−31390
3
( i − )∑
i=1
53 −32
7
25
2
= i − = i − 1∑
i=1
53 −32
7
∑
i=1
53 25
2
−32
7
∑
i=1
53 25
2
∑
i=1
53
= ⋅ − ⋅ 53 = ⋅ 1431 − ⋅ 53
−32
7
53 ⋅ (53 + 1)
2
25
2
−32
7
25
2
= − =
−45792
7
1325
2
−100859
14
(−15i − )∑
i=1
93 11
5
= −15i − = −15 i − 1 = −15 ⋅ − ⋅ 93∑
i=1
93
∑
i=1
93 11
5
∑
i=1
93 11
5
∑
i=1
93 93 ⋅ (93 + 1)
2
11
5
= −15 ⋅ 4371 − ⋅ 93 = −65565 − =
11
5
1023
5
−328848
5
( i − )∑
i=1
77
−25
9
19
10
= i − = i − 1∑
i=1
77
−25
9
∑
i=1
77 19
10
−25
9
∑
i=1
77 19
10
∑
i=1
77
= ⋅ − ⋅ 77 = ⋅ 3003 − ⋅ 77
−25
9
77 ⋅ (77 + 1)
2
19
10
−25
9
19
10
= − =
−25025
3
1463
10
−254639
30
180).
181).
182).
183).
184).
185).
186).
( i + )∑
i=1
80 23
2
38
7
= i + = i + 1∑
i=1
80 23
2
∑
i=1
80 38
7
23
2
∑
i=1
80 38
7
∑
i=1
80
= ⋅ + ⋅ 80 = ⋅ 3240 + ⋅ 80
23
2
80 ⋅ (80 + 1)
2
38
7
23
2
38
7
= 37260 + =
3040
7
263860
7
( i − )∑
i=1
95 −38
3
26
7
= i − = i − 1∑
i=1
95 −38
3
∑
i=1
95 26
7
−38
3
∑
i=1
95 26
7
∑
i=1
95
= ⋅ − ⋅ 95 = ⋅ 4560 − ⋅ 95
−38
3
95 ⋅ (95 + 1)
2
26
7
−38
3
26
7
= −57760 − =
2470
7
−406790
7
( i − )∑
i=1
61 −39
5
1
2
= i − = i − 1∑
i=1
61 −39
5
∑
i=1
61 1
2
−39
5
∑
i=1
61 1
2
∑
i=1
61
= ⋅ − ⋅ 61 = ⋅ 1891 − ⋅ 61
−39
5
61 ⋅ (61 + 1)
2
1
2
−39
5
1
2
= − =
−73749
5
61
2
−147803
10
( i − 10)∑
i=1
89 18
5
= i − 10 = i − 10 1 = ⋅ − 10 ⋅ 89∑
i=1
89 18
5
∑
i=1
89 18
5
∑
i=1
89
∑
i=1
89 18
5
89 ⋅ (89 + 1)
2
= ⋅ 4005 − 10 ⋅ 89 = 14418 − 890 = 13528
18
5
(−i + 12)∑
i=1
77
= −i + 12 = − i + 12 1 = − + 12 ⋅ 77 = −3003 + 924∑
i=1
77
∑
i=1
77
∑
i=1
77
∑
i=1
77 77 ⋅ (77 + 1)
2
= −2079
( i − )∑
i=1
81 1
5
23
4
= i − = i − 1∑
i=1
81 1
5
∑
i=1
81 23
4
1
5
∑
i=1
81 23
4
∑
i=1
81
= ⋅ − ⋅ 81 = ⋅ 3321 − ⋅ 81
1
5
81 ⋅ (81 + 1)
2
23
4
1
5
23
4
= − =
3321
5
1863
4
3969
20
( i + )∑
i=1
64 11
6
32
3
= i + = i + 1∑
i=1
64 11
6
∑
i=1
64 32
3
11
6
∑
i=1
64 32
3
∑
i=1
64
= ⋅ + ⋅ 64 = ⋅ 2080 + ⋅ 64
11
6
64 ⋅ (64 + 1)
2
32
3
11
6
32
3
= + = 4496
11440
3
2048
3
187).
188).
189).
190).
191).
192).
193).
( i + )∑
i=1
97 18
7
17
2
= i + = i + 1∑
i=1
97 18
7
∑
i=1
97 17
2
18
7
∑
i=1
97 17
2
∑
i=1
97
= ⋅ + ⋅ 97 = ⋅ 4753 + ⋅ 97
18
7
97 ⋅ (97 + 1)
2
17
2
18
7
17
2
= 12222 + =
1649
2
26093
2
( i − )∑
i=1
96 17
2
16
3
= i − = i − 1∑
i=1
96 17
2
∑
i=1
96 16
3
17
2
∑
i=1
96 16
3
∑
i=1
96
= ⋅ − ⋅ 96 = ⋅ 4656 − ⋅ 96
17
2
96 ⋅ (96 + 1)
2
16
3
17
2
16
3
= 39576 − 512 = 39064
( i − )∑
i=1
72 −8
9
27
2
= i − = i − 1∑
i=1
72 −8
9
∑
i=1
72 27
2
−8
9
∑
i=1
72 27
2
∑
i=1
72
= ⋅ − ⋅ 72 = ⋅ 2628 − ⋅ 72
−8
9
72 ⋅ (72 + 1)
2
27
2
−8
9
27
2
= −2336 − 972 = −3308
( i + )∑
i=1
53 −27
8
13
3
= i + = i + 1∑
i=1
53 −27
8
∑
i=1
53 13
3
−27
8
∑
i=1
53 13
3
∑
i=1
53
= ⋅ + ⋅ 53 = ⋅ 1431 + ⋅ 53
−27
8
53 ⋅ (53 + 1)
2
13
3
−27
8
13
3
= + =
−38637
8
689
3
−110399
24
( i + 4)∑
i=1
91 19
9
= i + 4 = i + 4 1 = ⋅ + 4 ⋅ 91∑
i=1
91 19
9
∑
i=1
91 19
9
∑
i=1
91
∑
i=1
91 19
9
91 ⋅ (91 + 1)
2
= ⋅ 4186 + 4 ⋅ 91 = + 364 =
19
9
79534
9
82810
9
( i + )∑
i=1
70 17
6
1
5
= i + = i + 1∑
i=1
70 17
6
∑
i=1
70 1
5
17
6
∑
i=1
70 1
5
∑
i=1
70
= ⋅ + ⋅ 70 = ⋅ 2485 + ⋅ 70
17
6
70 ⋅ (70 + 1)
2
1
5
17
6
1
5
= + 14 =
42245
6
42329
6
( i + )∑
i=1
50 −7
2
11
4
= i + = i + 1∑
i=1
50 −7
2
∑
i=1
50 11
4
−7
2
∑
i=1
50 11
4
∑
i=1
50
= ⋅ + ⋅ 50 = ⋅ 1275 + ⋅ 50
−7
2
50 ⋅ (50 + 1)
2
11
4
−7
2
11
4
= + = −4325
−8925
2
275
2
194).
195).
196).
197).
198).
199).
200).
( i + )∑
i=1
53
−17
2
36
7
= i + = i + 1∑
i=1
53 −17
2
∑
i=1
53 36
7
−17
2
∑
i=1
53 36
7
∑
i=1
53
= ⋅ + ⋅ 53 = ⋅ 1431 + ⋅ 53
−17
2
53 ⋅ (53 +1)
2
36
7
−17
2
36
7
= + =
−24327
2
1908
7
−166473
14
( i + )∑
i=1
61 19
5
37
9
= i + = i + 1∑
i=1
61 19
5
∑
i=1
61 37
9
19
5
∑
i=1
61 37
9
∑
i=1
61
= ⋅ + ⋅ 61 = ⋅ 1891 + ⋅ 61
19
5
61 ⋅ (61 + 1)
2
37
9
19
5
37
9
= + =
35929
5
2257
9
334646
45
( i + )∑
i=1
75 9
5
19
2
= i + = i + 1∑
i=1
75 9
5
∑
i=1
75 19
2
9
5
∑
i=1
75 19
2
∑
i=1
75
= ⋅ + ⋅ 75 = ⋅ 2850 + ⋅ 75
9
5
75 ⋅ (75 + 1)
2
19
2
9
5
19
2
= 5130 + =
1425
2
11685
2
(4i + 6)∑
i=1
78
= 4i + 6 = 4 i + 6 1 = 4 ⋅ + 6 ⋅ 78∑
i=1
78
∑
i=1
78
∑
i=1
78
∑
i=1
78 78 ⋅ (78 + 1)
2
= 4 ⋅ 3081 + 6 ⋅ 78 = 12324 + 468 = 12792
( i + )∑
i=1
69 24
5
43
2
= i + = i + 1∑
i=1
69 24
5
∑
i=1
69 43
2
24
5
∑
i=1
69 43
2
∑
i=1
69
= ⋅ + ⋅ 69 = ⋅ 2415 + ⋅ 69
24
5
69 ⋅ (69 + 1)
2
43
2
24
5
43
2
= 11592 + =
2967
2
26151
2
( i + )∑
i=1
92 29
6
22
5
= i + = i + 1∑
i=1
92 29
6
∑
i=1
92 22
5
29
6
∑
i=1
92 22
5
∑
i=1
92
= ⋅ + ⋅ 92 = ⋅ 4278 + ⋅ 92
29
6
92 ⋅ (92 + 1)
2
22
5
29
6
22
5
= 20677 + =
2024
5
105409
5
( i − )∑
i=1
55
−16
5
47
2
= i − = i − 1∑
i=1
55
−16
5
∑
i=1
55 47
2
−16
5
∑
i=1
55 47
2
∑
i=1
55
= ⋅ − ⋅ 55 = ⋅ 1540 − ⋅ 55
−16
5
55 ⋅ (55 + 1)
2
47
2
−16
5
47
2
= −4928 − =
2585
2
−12441
2