200 ejercicios sobre series resueltos paso por paso con todos los procedimientos.

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Series
Hallar el resultado de la suma de las siguientes series:
1). −21i =∑
i=1
81
2). 34i =∑
i=1
76
3). 50i =∑
i=1
77
4). 10i =∑
i=1
71
5). 20i =∑
i=1
84
6). 29i =∑
i=1
64
7). −i =∑
i=1
99
8). −6i =∑
i=1
65
9). −14i =∑
i=1
97
10). 46i =∑
i=1
98
11). 31i =∑
i=1
90
12). −7i =∑
i=1
94
13). −38i =∑
i=1
97
14). 8i =∑
i=1
72
15). 14i =∑
i=1
77
16). 16i =∑
i=1
71
17). 31i =∑
i=1
54
18). 24i =∑
i=1
54
19). 46i =∑
i=1
81
20). 18i =∑
i=1
81
21). −22i =∑
i=1
92
22). 46i =∑
i=1
82
23). 33i =∑
i=1
95
24). 18i =∑
i=1
81
25). 15i =∑
i=1
84
26). 36i =∑
i=1
68
27). −7i =∑
i=1
84
28). −24i =∑
i=1
95
29). 37i =∑
i=1
75
30). 41i =∑
i=1
100
31). 11i =∑
i=1
65
32). −23i =∑
i=1
83
33). 16i =∑
i=1
78
34). 4i =∑
i=1
72
35). 17i =∑
i=1
101
36). 18i =∑
i=1
84
37). −34i =∑
i=1
82
38). 6i =∑
i=1
83
39). −42i =∑
i=1
76
40). −30i =∑
i=1
78
41). 7i =∑
i=1
89
42). 14i =∑
i=1
53
43). −24i =∑
i=1
71
44). 41i =∑
i=1
77
45). −3i =∑
i=1
60
46). −i =∑
i=1
74
47). −41i =∑
i=1
80
48). 39i =∑
i=1
98
49). −23i =∑
i=1
88
50). 10i =∑
i=1
82
51). 29i =∑
i=1
59
52). 30i =∑
i=1
74
53). 32i =∑
i=1
55
54). 46i =∑
i=1
53
55). −6i =∑
i=1
61
56). 28i =∑
i=1
72
57). −39i =∑
i=1
61
58). −2i =∑
i=1
58
59). 6i =∑
i=1
72
60). 48i =∑
i=1
91
61). 8i =∑
i=1
72
62). −32i =∑
i=1
62
63). −19i =∑
i=1
69
64). 36i =∑
i=1
52
65). −27i =∑
i=1
84
66). −16i =∑
i=1
51
67). 33i =∑
i=1
79
68). i =∑
i=1
51
69). 42i =∑
i=1
84
70). −21i =∑
i=1
90
71). 44i =∑
i=1
59
72). −45i =∑
i=1
92
73). −20i =∑
i=1
53
74). −18i =∑
i=1
76
75). −31i =∑
i=1
87
76). 38i =∑
i=1
62
77). 29i =∑
i=1
84
78). −32i =∑
i=1
70
79). 4i =∑
i=1
77
80). 32i =∑
i=1
90
81). 2i =∑
i=1
53
82). −42i =∑
i=1
52
83). −33i =∑
i=1
90
84). 18i =∑
i=1
61
85). i =∑
i=1
54
86). 22i =∑
i=1
67
87). −35i =∑
i=1
72
88). 23i =∑
i=1
59
89). −44i =∑
i=1
64
90). 33i =∑
i=1
50
91). −2i =∑
i=1
51
92). 28i =∑
i=1
85
93). 25i =∑
i=1
66
94). 10i =∑
i=1
97
95). 37i =∑
i=1
65
96). −20i =∑
i=1
51
97). −30i =∑
i=1
67
98). 12i =∑
i=1
59
99). 14i =∑
i=1
101
100). −20i =∑
i=1
72
101). 48i =∑
i=1
83
102). 46i =∑
i=1
93
103). −39i =∑
i=1
92
104). 23i =∑
i=1
55
105). −16i =∑
i=1
94
106). 14i =∑
i=1
92
107). −8i =∑
i=1
72
108). 18i =∑
i=1
73
109). 24i =∑
i=1
100
110). −40i =∑
i=1
80
111). −33i =∑
i=1
56
112). −48i =∑
i=1
88
113). −20i =∑
i=1
94
114). 48i =∑
i=1
86
115). 22i =∑
i=1
65
116). 6i =∑
i=1
56
117). 2i =∑
i=1
91
118). −28i =∑
i=1
66
119). 41i =∑
i=1
92
120). −28i =∑
i=1
50
121). −49i =∑
i=1
98
122). 39i =∑
i=1
84
123). 10i =∑
i=1
63
124). −9i =∑
i=1
85
125). 5i =∑
i=1
77
126). −43i =∑
i=1
63
127). 36i =∑
i=1
86
128). −27i =∑
i=1
83
129). −16i =∑
i=1
79
130). 32i =∑
i=1
75
131). 47i =∑
i=1
67
132). 14i =∑
i=1
75
133). 23i =∑
i=1
98
134). 46i =∑
i=1
87
135). −44i =∑
i=1
58
136). 26i =∑
i=1
61
137). 42i =∑
i=1
60
138). 35i =∑
i=1
92
139). −22i =∑
i=1
95
140). −45i =∑
i=1
63
141). −37i =∑
i=1
91
142). 39i =∑
i=1
68
143). 34i =∑
i=1
66
144). −18i =∑
i=1
96
145). 34i =∑
i=1
73
146). −46i =∑
i=1
88
147). −35i =∑
i=1
52
148). −41i =∑
i=1
85
149). 30i =∑
i=1
99
150). i =∑
i=1
60
151). 38i =∑
i=1
82
152). 38i =∑
i=1
97
153). 32i =∑
i=1
100
154). −12i =∑
i=1
79
155). 46i =∑
i=1
99
156). −40i =∑
i=1
81
157). −20i =∑
i=1
54
158). 45i =∑
i=1
52
159). −30i =∑
i=1
51
160). 26i =∑
i=1
65
161). −15i =∑
i=1
97
162). 38i =∑
i=1
65
163). −36i =∑
i=1
101
164). −21i =∑
i=1
66
165). −34i =∑
i=1
97
166). 17i =∑
i=1
70
167). −37i =∑
i=1
66
168). 6i =∑
i=1
77
169). 3i =∑
i=1
57
170). −45i =∑
i=1
101
171). 17i =∑
i=1
84
172). 28i =∑
i=1
60
173). 5i =∑
i=1
74
174). 38i =∑
i=1
79
175). −13i =∑
i=1
50
176). i =∑
i=1
88
177). −16i =∑
i=1
75
178). −30i =∑
i=1
88
179). 47i =∑
i=1
98
180). −35i =∑
i=1
97
181). −21i =∑
i=1
71
182). 9i =∑
i=1
74
183). −41i =∑
i=1
50
184). −42i =∑
i=1
71
185). 37i =∑
i=1
97
186). −50i =∑
i=1
90
187). 29i =∑
i=1
68
188). i =∑
i=1
78
189). −27i =∑
i=1
79
190). 24i =∑
i=1
83
191). −2i =∑
i=1
56
192). −41i =∑
i=1
97
193). 28i =∑
i=1
93
194). −43i =∑
i=1
93
195). −29i =∑
i=1
98
196). −34i =∑
i=1
62
197). 41i =∑
i=1
61
198). −9i =∑
i=1
69
199). 17i =∑
i=1
89
200). −15i =∑
i=1
73
HOJA DE RESPUESTAS
Series
Hallar el resultado de la suma de las siguientes series:
1).
2).
3).
4).
5).
6).
7).
8).
9).
10).
11).
12).
−21i = −21 i = −21 ⋅ = −21 ⋅ 3321 = −69741∑
i=1
81
∑
i=1
81 81 ⋅ (81 + 1)
2
34i = 34 i = 34 ⋅ = 34 ⋅ 2926 = 99484∑
i=1
76
∑
i=1
76 76 ⋅ (76 + 1)
2
50i = 50 i = 50 ⋅ = 50 ⋅ 3003 = 150150∑
i=1
77
∑
i=1
77 77 ⋅ (77 + 1)
2
10i = 10 i = 10 ⋅ = 10 ⋅ 2556 = 25560∑
i=1
71
∑
i=1
71 71 ⋅ (71 + 1)
2
20i = 20 i = 20 ⋅ = 20 ⋅ 3570 = 71400∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
29i = 29 i = 29 ⋅ = 29 ⋅ 2080 = 60320∑
i=1
64
∑
i=1
64 64 ⋅ (64 + 1)
2
−i = − i = − = −4950∑
i=1
99
∑
i=1
99 99 ⋅ (99 + 1)
2
−6i = −6 i = −6 ⋅ = −6 ⋅ 2145 = −12870∑
i=1
65
∑
i=1
65 65 ⋅ (65 + 1)
2
−14i = −14 i = −14 ⋅ = −14 ⋅ 4753 = −66542∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
46i = 46 i = 46 ⋅ = 46 ⋅ 4851 = 223146∑
i=1
98
∑
i=1
98 98 ⋅ (98 + 1)
2
31i = 31 i = 31 ⋅ = 31 ⋅ 4095 = 126945∑
i=1
90
∑
i=1
90 90 ⋅ (90 + 1)
2
−7i = −7 i = −7 ⋅ = −7 ⋅ 4465 = −31255∑
i=1
94
∑
i=1
94 94 ⋅ (94 + 1)
2
13).
14).
15).
16).
17).
18).
19).
20).
21).
22).
23).
24).
25).
−38i = −38 i = −38 ⋅ = −38 ⋅ 4753 = −180614∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
8i = 8 i = 8 ⋅ = 8 ⋅ 2628 = 21024∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
14i = 14 i = 14 ⋅ = 14 ⋅ 3003 = 42042∑
i=1
77
∑
i=1
77 77 ⋅ (77 + 1)
2
16i = 16 i = 16 ⋅ = 16 ⋅ 2556 = 40896∑
i=1
71
∑
i=1
71 71 ⋅ (71 + 1)
2
31i = 31 i = 31 ⋅ = 31 ⋅ 1485 = 46035∑
i=1
54
∑
i=1
54 54 ⋅ (54 + 1)
2
24i = 24 i = 24 ⋅ = 24 ⋅ 1485 = 35640∑
i=1
54
∑
i=1
54 54 ⋅ (54 + 1)
2
46i = 46 i = 46 ⋅ = 46 ⋅ 3321 = 152766∑
i=1
81
∑
i=1
81 81 ⋅ (81 + 1)
2
18i = 18 i = 18 ⋅ = 18 ⋅ 3321 = 59778∑
i=1
81
∑
i=1
81 81 ⋅ (81 + 1)
2
−22i = −22 i = −22 ⋅ = −22 ⋅ 4278 = −94116∑
i=1
92
∑
i=1
92 92 ⋅ (92 + 1)
2
46i = 46 i = 46 ⋅ = 46 ⋅ 3403 = 156538∑
i=1
82
∑
i=1
82 82 ⋅ (82 + 1)
2
33i = 33 i = 33 ⋅ = 33 ⋅ 4560 = 150480∑
i=1
95
∑
i=1
95 95 ⋅ (95 + 1)
2
18i = 18 i = 18 ⋅ = 18 ⋅ 3321 = 59778∑
i=1
81
∑
i=1
81 81 ⋅ (81 + 1)
2
15i = 15 i = 15 ⋅ = 15 ⋅ 3570 = 53550∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
26).
27).
28).
29).
30).
31).
32).
33).
34).
35).
36).
37).
38).
36i = 36 i = 36 ⋅ = 36 ⋅ 2346 = 84456∑
i=1
68
∑
i=1
68 68 ⋅ (68 + 1)
2
−7i = −7 i = −7 ⋅ = −7 ⋅ 3570 = −24990∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
−24i = −24 i = −24 ⋅ = −24 ⋅ 4560 = −109440∑
i=1
95
∑
i=1
95 95 ⋅ (95 + 1)
2
37i = 37 i = 37 ⋅ = 37 ⋅ 2850 = 105450∑
i=1
75
∑
i=1
75 75 ⋅ (75 + 1)
2
41i = 41 i = 41 ⋅ = 41 ⋅ 5050 = 207050∑
i=1
100
∑
i=1
100 100 ⋅ (100 + 1)
2
11i = 11 i = 11 ⋅ = 11 ⋅ 2145 = 23595∑
i=1
65
∑
i=1
65 65 ⋅ (65 + 1)
2
−23i = −23 i = −23 ⋅ = −23 ⋅ 3486 = −80178∑
i=1
83
∑
i=1
83 83 ⋅ (83 + 1)
2
16i = 16 i = 16 ⋅ = 16 ⋅ 3081 = 49296∑
i=1
78
∑
i=1
78 78 ⋅ (78 + 1)
2
4i = 4 i = 4 ⋅ = 4 ⋅ 2628 = 10512∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
17i = 17 i = 17 ⋅ = 17 ⋅ 5151 = 87567∑
i=1
101
∑
i=1
101 101 ⋅ (101 + 1)
2
18i = 18 i = 18 ⋅ = 18 ⋅ 3570 = 64260∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
−34i = −34 i = −34 ⋅ = −34 ⋅ 3403 = −115702∑
i=1
82
∑
i=1
82 82 ⋅ (82 + 1)
2
6i = 6 i = 6 ⋅ = 6 ⋅ 3486 = 20916∑
i=1
83
∑
i=1
83 83 ⋅ (83 + 1)
2
39).
40).
41).
42).
43).
44).
45).
46).
47).
48).
49).
50).
51).
−42i = −42 i = −42 ⋅ = −42 ⋅ 2926 = −122892∑
i=1
76
∑
i=1
76 76 ⋅ (76 + 1)
2
−30i = −30 i = −30 ⋅ = −30 ⋅ 3081 = −92430∑
i=1
78
∑
i=1
78 78 ⋅ (78 + 1)
2
7i = 7 i = 7 ⋅ = 7 ⋅ 4005 = 28035∑
i=1
89
∑
i=1
89 89 ⋅ (89 + 1)
2
14i = 14 i = 14 ⋅ = 14 ⋅ 1431 = 20034∑
i=1
53
∑
i=1
53 53 ⋅ (53 + 1)
2
−24i = −24 i =−24 ⋅ = −24 ⋅ 2556 = −61344∑
i=1
71
∑
i=1
71 71 ⋅ (71 + 1)
2
41i = 41 i = 41 ⋅ = 41 ⋅ 3003 = 123123∑
i=1
77
∑
i=1
77 77 ⋅ (77 + 1)
2
−3i = −3 i = −3 ⋅ = −3 ⋅ 1830 = −5490∑
i=1
60
∑
i=1
60 60 ⋅ (60 + 1)
2
−i = − i = − = −2775∑
i=1
74
∑
i=1
74 74 ⋅ (74 + 1)
2
−41i = −41 i = −41 ⋅ = −41 ⋅ 3240 = −132840∑
i=1
80
∑
i=1
80 80 ⋅ (80 + 1)
2
39i = 39 i = 39 ⋅ = 39 ⋅ 4851 = 189189∑
i=1
98
∑
i=1
98 98 ⋅ (98 + 1)
2
−23i = −23 i = −23 ⋅ = −23 ⋅ 3916 = −90068∑
i=1
88
∑
i=1
88 88 ⋅ (88 + 1)
2
10i = 10 i = 10 ⋅ = 10 ⋅ 3403 = 34030∑
i=1
82
∑
i=1
82 82 ⋅ (82 + 1)
2
29i = 29 i = 29 ⋅ = 29 ⋅ 1770 = 51330∑
i=1
59
∑
i=1
59 59 ⋅ (59 + 1)
2
52).
53).
54).
55).
56).
57).
58).
59).
60).
61).
62).
63).
64).
30i = 30 i = 30 ⋅ = 30 ⋅ 2775 = 83250∑
i=1
74
∑
i=1
74 74 ⋅ (74 + 1)
2
32i = 32 i = 32 ⋅ = 32 ⋅ 1540 = 49280∑
i=1
55
∑
i=1
55 55 ⋅ (55 + 1)
2
46i = 46 i = 46 ⋅ = 46 ⋅ 1431 = 65826∑
i=1
53
∑
i=1
53 53 ⋅ (53 + 1)
2
−6i = −6 i = −6 ⋅ = −6 ⋅ 1891 = −11346∑
i=1
61
∑
i=1
61 61 ⋅ (61 + 1)
2
28i = 28 i = 28 ⋅ = 28 ⋅ 2628 = 73584∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
−39i = −39 i = −39 ⋅ = −39 ⋅ 1891 = −73749∑
i=1
61
∑
i=1
61 61 ⋅ (61 + 1)
2
−2i = −2 i = −2 ⋅ = −2 ⋅ 1711 = −3422∑
i=1
58
∑
i=1
58 58 ⋅ (58 + 1)
2
6i = 6 i = 6 ⋅ = 6 ⋅ 2628 = 15768∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
48i = 48 i = 48 ⋅ = 48 ⋅ 4186 = 200928∑
i=1
91
∑
i=1
91 91 ⋅ (91 + 1)
2
8i = 8 i = 8 ⋅ = 8 ⋅ 2628 = 21024∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
−32i = −32 i = −32 ⋅ = −32 ⋅ 1953 = −62496∑
i=1
62
∑
i=1
62 62 ⋅ (62 + 1)
2
−19i = −19 i = −19 ⋅ = −19 ⋅ 2415 = −45885∑
i=1
69
∑
i=1
69 69 ⋅ (69 + 1)
2
36i = 36 i = 36 ⋅ = 36 ⋅ 1378 = 49608∑
i=1
52
∑
i=1
52 52 ⋅ (52 + 1)
2
65).
66).
67).
68).
69).
70).
71).
72).
73).
74).
75).
76).
77).
−27i = −27 i = −27 ⋅ = −27 ⋅ 3570 = −96390∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
−16i = −16 i = −16 ⋅ = −16 ⋅ 1326 = −21216∑
i=1
51
∑
i=1
51 51 ⋅ (51 + 1)
2
33i = 33 i = 33 ⋅ = 33 ⋅ 3160 = 104280∑
i=1
79
∑
i=1
79 79 ⋅ (79 + 1)
2
i = = 1326∑
i=1
51 51 ⋅ (51 + 1)
2
42i = 42 i = 42 ⋅ = 42 ⋅ 3570 = 149940∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
−21i = −21 i = −21 ⋅ = −21 ⋅ 4095 = −85995∑
i=1
90
∑
i=1
90 90 ⋅ (90 + 1)
2
44i = 44 i = 44 ⋅ = 44 ⋅ 1770 = 77880∑
i=1
59
∑
i=1
59 59 ⋅ (59 + 1)
2
−45i = −45 i = −45 ⋅ = −45 ⋅ 4278 = −192510∑
i=1
92
∑
i=1
92 92 ⋅ (92 + 1)
2
−20i = −20 i = −20 ⋅ = −20 ⋅ 1431 = −28620∑
i=1
53
∑
i=1
53 53 ⋅ (53 + 1)
2
−18i = −18 i = −18 ⋅ = −18 ⋅ 2926 = −52668∑
i=1
76
∑
i=1
76 76 ⋅ (76 + 1)
2
−31i = −31 i = −31 ⋅ = −31 ⋅ 3828 = −118668∑
i=1
87
∑
i=1
87 87 ⋅ (87 + 1)
2
38i = 38 i = 38 ⋅ = 38 ⋅ 1953 = 74214∑
i=1
62
∑
i=1
62 62 ⋅ (62 + 1)
2
29i = 29 i = 29 ⋅ = 29 ⋅ 3570 = 103530∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
78).
79).
80).
81).
82).
83).
84).
85).
86).
87).
88).
89).
90).
−32i = −32 i = −32 ⋅ = −32 ⋅ 2485 = −79520∑
i=1
70
∑
i=1
70 70 ⋅ (70 + 1)
2
4i = 4 i = 4 ⋅ = 4 ⋅ 3003 = 12012∑
i=1
77
∑
i=1
77 77 ⋅ (77 + 1)
2
32i = 32 i = 32 ⋅ = 32 ⋅ 4095 = 131040∑
i=1
90
∑
i=1
90 90 ⋅ (90 + 1)
2
2i = 2 i = 2 ⋅ = 2 ⋅ 1431 = 2862∑
i=1
53
∑
i=1
53 53 ⋅ (53 + 1)
2
−42i = −42 i = −42 ⋅ = −42 ⋅ 1378 = −57876∑
i=1
52
∑
i=1
52 52 ⋅ (52 + 1)
2
−33i = −33 i = −33 ⋅ = −33 ⋅ 4095 = −135135∑
i=1
90
∑
i=1
90 90 ⋅ (90 + 1)
2
18i = 18 i = 18 ⋅ = 18 ⋅ 1891 = 34038∑
i=1
61
∑
i=1
61 61 ⋅ (61 + 1)
2
i = = 1485∑
i=1
54 54 ⋅ (54 + 1)
2
22i = 22 i = 22 ⋅ = 22 ⋅ 2278 = 50116∑
i=1
67
∑
i=1
67 67 ⋅ (67 + 1)
2
−35i = −35 i = −35 ⋅ = −35 ⋅ 2628 = −91980∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
23i = 23 i = 23 ⋅ = 23 ⋅ 1770 = 40710∑
i=1
59
∑
i=1
59 59 ⋅ (59 + 1)
2
−44i = −44 i = −44 ⋅ = −44 ⋅ 2080 = −91520∑
i=1
64
∑
i=1
64 64 ⋅ (64 + 1)
2
33i = 33 i = 33 ⋅ = 33 ⋅ 1275 = 42075∑
i=1
50
∑
i=1
50 50 ⋅ (50 + 1)
2
91).
92).
93).
94).
95).
96).
97).
98).
99).
100).
101).
102).
103).
−2i = −2 i = −2 ⋅ = −2 ⋅ 1326 = −2652∑
i=1
51
∑
i=1
51 51 ⋅ (51 + 1)
2
28i = 28 i = 28 ⋅ = 28 ⋅ 3655 = 102340∑
i=1
85
∑
i=1
85 85 ⋅ (85 + 1)
2
25i = 25 i = 25 ⋅ = 25 ⋅ 2211 = 55275∑
i=1
66
∑
i=1
66 66 ⋅ (66 + 1)
2
10i = 10 i = 10 ⋅ = 10 ⋅ 4753 = 47530∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
37i = 37 i = 37 ⋅ = 37 ⋅ 2145 = 79365∑
i=1
65
∑
i=1
65 65 ⋅ (65 + 1)
2
−20i = −20 i = −20 ⋅ = −20 ⋅ 1326 = −26520∑
i=1
51
∑
i=1
51 51 ⋅ (51 + 1)
2
−30i = −30 i = −30 ⋅ = −30 ⋅ 2278 = −68340∑
i=1
67
∑
i=1
67 67 ⋅ (67 + 1)
2
12i = 12 i = 12 ⋅ = 12 ⋅ 1770 = 21240∑
i=1
59
∑
i=1
59 59 ⋅ (59 + 1)
2
14i = 14 i = 14 ⋅ = 14 ⋅ 5151 = 72114∑
i=1
101
∑
i=1
101 101 ⋅ (101 + 1)
2
−20i = −20 i = −20 ⋅ = −20 ⋅ 2628 = −52560∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
48i = 48 i = 48 ⋅ = 48 ⋅ 3486 = 167328∑
i=1
83
∑
i=1
83 83 ⋅ (83 + 1)
2
46i = 46 i = 46 ⋅ = 46 ⋅ 4371 = 201066∑
i=1
93
∑
i=1
93 93 ⋅ (93 + 1)
2
−39i = −39 i = −39 ⋅ = −39 ⋅ 4278 = −166842∑
i=1
92
∑
i=1
92 92 ⋅ (92 + 1)
2
104).
105).
106).
107).
108).
109).
110).
111).
112).
113).
114).
115).
116).
23i = 23 i = 23 ⋅ = 23 ⋅ 1540 = 35420∑
i=1
55
∑
i=1
55 55 ⋅ (55 + 1)
2
−16i = −16 i = −16 ⋅ = −16 ⋅ 4465 = −71440∑
i=1
94
∑
i=1
94 94 ⋅ (94 + 1)
2
14i = 14 i = 14 ⋅ = 14 ⋅ 4278 = 59892∑
i=1
92
∑
i=1
92 92 ⋅ (92 + 1)
2
−8i = −8 i = −8 ⋅ = −8 ⋅ 2628 = −21024∑
i=1
72
∑
i=1
72 72 ⋅ (72 + 1)
2
18i = 18 i = 18 ⋅ = 18 ⋅ 2701 = 48618∑
i=1
73
∑
i=1
73 73 ⋅ (73 + 1)
2
24i = 24 i = 24 ⋅ = 24 ⋅ 5050 = 121200∑
i=1
100
∑
i=1
100 100 ⋅ (100 + 1)
2
−40i = −40 i = −40 ⋅ = −40 ⋅ 3240 = −129600∑
i=1
80
∑
i=1
80 80 ⋅ (80 + 1)
2
−33i = −33 i = −33 ⋅ = −33 ⋅ 1596 = −52668∑
i=1
56
∑
i=1
56 56 ⋅ (56 + 1)
2
−48i = −48 i = −48 ⋅ = −48 ⋅ 3916 = −187968∑
i=1
88
∑
i=1
88 88 ⋅ (88 + 1)
2
−20i = −20 i = −20 ⋅ = −20 ⋅ 4465 = −89300∑
i=1
94
∑
i=1
94 94 ⋅ (94 + 1)
2
48i = 48 i = 48 ⋅ = 48 ⋅ 3741 = 179568∑
i=1
86
∑
i=1
86 86 ⋅ (86 + 1)
2
22i = 22 i = 22 ⋅ = 22 ⋅ 2145 = 47190∑
i=1
65
∑
i=1
65 65 ⋅ (65 + 1)
2
6i = 6 i = 6 ⋅ = 6 ⋅ 1596 = 9576∑
i=1
56
∑
i=1
56 56 ⋅ (56 + 1)
2
117).
118).
119).
120).
121).
122).
123).
124).
125).
126).
127).
128).
129).
2i = 2 i = 2 ⋅ = 2 ⋅ 4186 = 8372∑
i=1
91
∑
i=1
91 91 ⋅ (91 + 1)
2
−28i = −28 i = −28 ⋅ = −28 ⋅ 2211 = −61908∑
i=1
66
∑
i=1
66 66 ⋅ (66 + 1)
2
41i = 41 i = 41 ⋅ = 41 ⋅ 4278 = 175398∑
i=1
92
∑
i=1
92 92 ⋅ (92 + 1)
2
−28i = −28 i = −28 ⋅ = −28 ⋅ 1275 = −35700∑
i=1
50
∑
i=1
50 50 ⋅ (50 + 1)
2
−49i = −49 i = −49 ⋅ = −49 ⋅ 4851 = −237699∑
i=1
98
∑
i=1
98 98 ⋅ (98 + 1)
2
39i = 39 i = 39 ⋅ = 39 ⋅ 3570 = 139230∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
10i = 10 i = 10 ⋅ = 10 ⋅ 2016 = 20160∑
i=1
63
∑
i=1
63 63 ⋅ (63 + 1)
2
−9i = −9 i = −9 ⋅ = −9 ⋅ 3655 = −32895∑
i=1
85
∑
i=1
85 85 ⋅ (85 + 1)
2
5i = 5 i = 5 ⋅ = 5 ⋅ 3003 = 15015∑
i=1
77
∑
i=1
77 77 ⋅ (77 + 1)
2
−43i = −43 i = −43 ⋅ = −43 ⋅ 2016 = −86688∑
i=1
63
∑
i=1
63 63 ⋅ (63 + 1)
2
36i = 36 i = 36 ⋅ = 36 ⋅ 3741 = 134676∑
i=1
86
∑
i=1
86 86 ⋅ (86 + 1)
2
−27i = −27 i = −27 ⋅ = −27 ⋅ 3486 = −94122∑
i=1
83
∑
i=1
83 83 ⋅ (83 + 1)
2
−16i = −16 i = −16 ⋅ = −16 ⋅ 3160 = −50560∑
i=1
79
∑
i=1
79 79 ⋅ (79 + 1)
2
130).
131).
132).
133).
134).
135).
136).
137).
138).
139).
140).
141).
142).
32i = 32 i = 32 ⋅ = 32 ⋅ 2850 = 91200∑
i=1
75
∑
i=1
75 75 ⋅ (75 + 1)
2
47i = 47 i = 47 ⋅ = 47 ⋅ 2278 = 107066∑
i=1
67
∑
i=1
67 67 ⋅ (67 + 1)
2
14i = 14 i = 14 ⋅ = 14 ⋅ 2850 = 39900∑
i=1
75
∑
i=1
75 75 ⋅ (75 + 1)
2
23i = 23 i = 23 ⋅ = 23 ⋅ 4851 = 111573∑
i=1
98
∑
i=1
98 98 ⋅ (98 + 1)
2
46i = 46 i = 46 ⋅ = 46 ⋅ 3828 = 176088∑
i=1
87
∑
i=1
87 87 ⋅ (87 + 1)
2
−44i = −44 i = −44 ⋅ = −44 ⋅ 1711 = −75284∑
i=1
58
∑
i=1
58 58 ⋅ (58 + 1)
2
26i = 26 i = 26 ⋅ = 26 ⋅ 1891 = 49166∑
i=1
61
∑
i=1
61 61 ⋅ (61 + 1)
2
42i = 42 i = 42 ⋅ = 42 ⋅ 1830 = 76860∑
i=1
60
∑
i=1
60 60 ⋅ (60 + 1)
2
35i = 35 i = 35 ⋅ = 35 ⋅ 4278 = 149730∑
i=1
92
∑
i=1
92 92 ⋅ (92 + 1)
2
−22i = −22 i = −22 ⋅ = −22 ⋅ 4560 = −100320∑
i=1
95
∑
i=1
95 95 ⋅ (95 + 1)2
−45i = −45 i = −45 ⋅ = −45 ⋅ 2016 = −90720∑
i=1
63
∑
i=1
63 63 ⋅ (63 + 1)
2
−37i = −37 i = −37 ⋅ = −37 ⋅ 4186 = −154882∑
i=1
91
∑
i=1
91 91 ⋅ (91 + 1)
2
39i = 39 i = 39 ⋅ = 39 ⋅ 2346 = 91494∑
i=1
68
∑
i=1
68 68 ⋅ (68 + 1)
2
143).
144).
145).
146).
147).
148).
149).
150).
151).
152).
153).
154).
155).
34i = 34 i = 34 ⋅ = 34 ⋅ 2211 = 75174∑
i=1
66
∑
i=1
66 66 ⋅ (66 + 1)
2
−18i = −18 i = −18 ⋅ = −18 ⋅ 4656 = −83808∑
i=1
96
∑
i=1
96 96 ⋅ (96 + 1)
2
34i = 34 i = 34 ⋅ = 34 ⋅ 2701 = 91834∑
i=1
73
∑
i=1
73 73 ⋅ (73 + 1)
2
−46i = −46 i = −46 ⋅ = −46 ⋅ 3916 = −180136∑
i=1
88
∑
i=1
88 88 ⋅ (88 + 1)
2
−35i = −35 i = −35 ⋅ = −35 ⋅ 1378 = −48230∑
i=1
52
∑
i=1
52 52 ⋅ (52 + 1)
2
−41i = −41 i = −41 ⋅ = −41 ⋅ 3655 = −149855∑
i=1
85
∑
i=1
85 85 ⋅ (85 + 1)
2
30i = 30 i = 30 ⋅ = 30 ⋅ 4950 = 148500∑
i=1
99
∑
i=1
99 99 ⋅ (99 + 1)
2
i = = 1830∑
i=1
60 60 ⋅ (60 + 1)
2
38i = 38 i = 38 ⋅ = 38 ⋅ 3403 = 129314∑
i=1
82
∑
i=1
82 82 ⋅ (82 + 1)
2
38i = 38 i = 38 ⋅ = 38 ⋅ 4753 = 180614∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
32i = 32 i = 32 ⋅ = 32 ⋅ 5050 = 161600∑
i=1
100
∑
i=1
100 100 ⋅ (100 + 1)
2
−12i = −12 i = −12 ⋅ = −12 ⋅ 3160 = −37920∑
i=1
79
∑
i=1
79 79 ⋅ (79 + 1)
2
46i = 46 i = 46 ⋅ = 46 ⋅ 4950 = 227700∑
i=1
99
∑
i=1
99 99 ⋅ (99 + 1)
2
156).
157).
158).
159).
160).
161).
162).
163).
164).
165).
166).
167).
168).
−40i = −40 i = −40 ⋅ = −40 ⋅ 3321 = −132840∑
i=1
81
∑
i=1
81 81 ⋅ (81 + 1)
2
−20i = −20 i = −20 ⋅ = −20 ⋅ 1485 = −29700∑
i=1
54
∑
i=1
54 54 ⋅ (54 + 1)
2
45i = 45 i = 45 ⋅ = 45 ⋅ 1378 = 62010∑
i=1
52
∑
i=1
52 52 ⋅ (52 + 1)
2
−30i = −30 i = −30 ⋅ = −30 ⋅ 1326 = −39780∑
i=1
51
∑
i=1
51 51 ⋅ (51 + 1)
2
26i = 26 i = 26 ⋅ = 26 ⋅ 2145 = 55770∑
i=1
65
∑
i=1
65 65 ⋅ (65 + 1)
2
−15i = −15 i = −15 ⋅ = −15 ⋅ 4753 = −71295∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
38i = 38 i = 38 ⋅ = 38 ⋅ 2145 = 81510∑
i=1
65
∑
i=1
65 65 ⋅ (65 + 1)
2
−36i = −36 i = −36 ⋅ = −36 ⋅ 5151 = −185436∑
i=1
101
∑
i=1
101 101 ⋅ (101 + 1)
2
−21i = −21 i = −21 ⋅ = −21 ⋅ 2211 = −46431∑
i=1
66
∑
i=1
66 66 ⋅ (66 + 1)
2
−34i = −34 i = −34 ⋅ = −34 ⋅ 4753 = −161602∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
17i = 17 i = 17 ⋅ = 17 ⋅ 2485 = 42245∑
i=1
70
∑
i=1
70 70 ⋅ (70 + 1)
2
−37i = −37 i = −37 ⋅ = −37 ⋅ 2211 = −81807∑
i=1
66
∑
i=1
66 66 ⋅ (66 + 1)
2
6i = 6 i = 6 ⋅ = 6 ⋅ 3003 = 18018∑
i=1
77
∑
i=1
77 77 ⋅ (77 + 1)
2
169).
170).
171).
172).
173).
174).
175).
176).
177).
178).
179).
180).
181).
3i = 3 i = 3 ⋅ = 3 ⋅ 1653 = 4959∑
i=1
57
∑
i=1
57 57 ⋅ (57 + 1)
2
−45i = −45 i = −45 ⋅ = −45 ⋅ 5151 = −231795∑
i=1
101
∑
i=1
101 101 ⋅ (101 + 1)
2
17i = 17 i = 17 ⋅ = 17 ⋅ 3570 = 60690∑
i=1
84
∑
i=1
84 84 ⋅ (84 + 1)
2
28i = 28 i = 28 ⋅ = 28 ⋅ 1830 = 51240∑
i=1
60
∑
i=1
60 60 ⋅ (60 + 1)
2
5i = 5 i = 5 ⋅ = 5 ⋅ 2775 = 13875∑
i=1
74
∑
i=1
74 74 ⋅ (74 + 1)
2
38i = 38 i = 38 ⋅ = 38 ⋅ 3160 = 120080∑
i=1
79
∑
i=1
79 79 ⋅ (79 + 1)
2
−13i = −13 i = −13 ⋅ = −13 ⋅ 1275 = −16575∑
i=1
50
∑
i=1
50 50 ⋅ (50 + 1)
2
i = = 3916∑
i=1
88 88 ⋅ (88 + 1)
2
−16i = −16 i = −16 ⋅ = −16 ⋅ 2850 = −45600∑
i=1
75
∑
i=1
75 75 ⋅ (75 + 1)
2
−30i = −30 i = −30 ⋅ = −30 ⋅ 3916 = −117480∑
i=1
88
∑
i=1
88 88 ⋅ (88 + 1)
2
47i = 47 i = 47 ⋅ = 47 ⋅ 4851 = 227997∑
i=1
98
∑
i=1
98 98 ⋅ (98 + 1)
2
−35i = −35 i = −35 ⋅ = −35 ⋅ 4753 = −166355∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
−21i = −21 i = −21 ⋅ = −21 ⋅ 2556 = −53676∑
i=1
71
∑
i=1
71 71 ⋅ (71 + 1)
2
182).
183).
184).
185).
186).
187).
188).
189).
190).
191).
192).
193).
194).
9i = 9 i = 9 ⋅ = 9 ⋅ 2775 = 24975∑
i=1
74
∑
i=1
74 74 ⋅ (74 + 1)
2
−41i = −41 i = −41 ⋅ = −41 ⋅ 1275 = −52275∑
i=1
50
∑
i=1
50 50 ⋅ (50 + 1)
2
−42i = −42 i = −42 ⋅ = −42 ⋅ 2556 = −107352∑
i=1
71
∑
i=1
71 71 ⋅ (71 + 1)
2
37i = 37 i = 37 ⋅ = 37 ⋅ 4753 = 175861∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
−50i = −50 i = −50 ⋅ = −50 ⋅ 4095 = −204750∑
i=1
90
∑
i=1
90 90 ⋅ (90 + 1)
2
29i = 29 i = 29 ⋅ = 29 ⋅ 2346 = 68034∑
i=1
68
∑
i=1
68 68 ⋅ (68 + 1)
2
i = = 3081∑
i=1
78 78 ⋅ (78 + 1)
2
−27i = −27 i = −27 ⋅ = −27 ⋅ 3160 = −85320∑
i=1
79
∑
i=1
79 79 ⋅ (79 + 1)
2
24i = 24 i = 24 ⋅ = 24 ⋅ 3486 = 83664∑
i=1
83
∑
i=1
83 83 ⋅ (83 + 1)
2
−2i = −2 i = −2 ⋅ = −2 ⋅ 1596 = −3192∑
i=1
56
∑
i=1
56 56 ⋅ (56 + 1)
2
−41i = −41 i = −41 ⋅ = −41 ⋅ 4753 = −194873∑
i=1
97
∑
i=1
97 97 ⋅ (97 + 1)
2
28i = 28 i = 28 ⋅ = 28 ⋅ 4371 = 122388∑
i=1
93
∑
i=1
93 93 ⋅ (93 + 1)
2
−43i = −43 i = −43 ⋅ = −43 ⋅ 4371 = −187953∑
i=1
93
∑
i=1
93 93 ⋅ (93 + 1)
2
195).
196).
197).
198).
199).
200).
−29i = −29 i = −29 ⋅ = −29 ⋅ 4851 = −140679∑
i=1
98
∑
i=1
98 98 ⋅ (98 + 1)
2
−34i = −34 i = −34 ⋅ = −34 ⋅ 1953 = −66402∑
i=1
62
∑
i=1
62 62 ⋅ (62 + 1)
2
41i = 41 i = 41 ⋅ = 41 ⋅ 1891 = 77531∑
i=1
61
∑
i=1
61 61 ⋅ (61 + 1)
2
−9i = −9 i = −9 ⋅ = −9 ⋅ 2415 = −21735∑
i=1
69
∑
i=1
69 69 ⋅ (69 + 1)
2
17i = 17 i = 17 ⋅ = 17 ⋅ 4005 = 68085∑
i=1
89
∑
i=1
89 89 ⋅ (89 + 1)
2
−15i = −15 i = −15 ⋅ = −15 ⋅ 2701 = −40515∑
i=1
73
∑
i=1
73 73 ⋅ (73 + 1)
2