Question

Rewrite $\sum_{n=1}^k{(n-1)/n!}$ and write the formula in terms of k

score 59 · Answer 1 · 2026-04-13 05:28:28

59

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Rewrite $\sum_{n=1}^k{(n-1)/n!}$ and write the formula in terms of k

Published on 13 Apr 2026 - 5:28

score 53 · Answer 2 · 2026-04-15 05:51:15

53

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Rewrite $\sum_{n=1}^k\log_3{(\frac{n+1}{n})}$ and write the formula in terms of k

Published on 15 Apr 2026 - 5:51

score 106 · Answer 3 · 2026-04-16 04:30:32

106

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Find $ \cot\left(\sum_{n=1}^{23} \cot^{-1} (1+\sum_{k=1}^n 2k )\right)$

Published on 16 Apr 2026 - 4:30

score 1.6k · Answer 4 · 2026-04-09 10:11:28

1.6k

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How does one transform a sum into a telescoping sum?

Published on 09 Apr 2026 - 10:11

score 63 · Answer 5 · 2026-04-11 04:45:40

63

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Help needed in understanding the telescoping sum for series $(a-b)\sum_{i=0}^{n-1}a^ib^{n-1-i}$.

Published on 11 Apr 2026 - 4:45

score 269 · Answer 6 · 2026-04-15 21:45:57

269

Views

How to prove $a^n − b^n = (a − b) \sum_{i=1}^{n}a^{n-i} b^{i-1}\le (a − b)na^{n−1}$.

Published on 15 Apr 2026 - 21:45

score 1.1k · Answer 7 · 2026-04-12 15:56:12

1.1k

Views

Proof of Telescoping Series

Published on 12 Apr 2026 - 15:56

score 599 · Answer 8 · 2026-04-16 13:24:18

599

Views

Proving inequality for induction proof: $\frac1{(n+1)^2} + \frac1{n+1} < \frac1n$

Published on 16 Apr 2026 - 13:24

score 129 · Answer 9 · 2026-04-15 13:45:34

129

Views

Telescoping series seems not telescoping

Published on 15 Apr 2026 - 13:45

score 648 · Answer 10 · 2026-04-14 07:14:12

648

Views

Convergence and Divergence in $2^{-\ln n}$

Published on 14 Apr 2026 - 7:14

score 59 · Answer 11 · 2026-04-14 04:58:32

59

Views

Limit of a sum that seems telescopable

Published on 14 Apr 2026 - 4:58

score 165 · Answer 12 · 2026-04-17 02:37:58

165

Views

Computing $\frac{\sin(3)}{\cos(0)\cos(3)}+\frac{\sin(3)}{\cos(3)\cos(6)} +\cdots+\frac{\sin(3)}{\cos(42)\cos(45)}$

Published on 17 Apr 2026 - 2:37

score 130 · Answer 13 · 2026-04-15 18:50:47

130

Views

Find, analytically, the value of the following limit.

Published on 15 Apr 2026 - 18:50

score 1k · Answer 14 · 2026-04-16 15:26:49

1k

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$S_n = \sum_{r=0}^{n-1} \cos^{-1} ( \frac{n^2+r^2+r}{\sqrt{n^4 +r^4+2r^3+2n^2r^2+2n^2r+n^2+r^2}})$ find$S_{100}$

Published on 16 Apr 2026 - 15:26

score 101 · Answer 15 · 2026-04-14 03:03:15

101

Views

How to find $\sum_{r=1}^{n}\frac{1}{T_r}$ when $\sum_{r=1}^{n}T_r$ is given?

Published on 14 Apr 2026 - 3:03

List Question

Rewrite $\sum_{n=1}^k{(n-1)/n!}$ and write the formula in terms of k

Rewrite $\sum_{n=1}^k\log_3{(\frac{n+1}{n})}$ and write the formula in terms of k

Find $ \cot\left(\sum_{n=1}^{23} \cot^{-1} (1+\sum_{k=1}^n 2k )\right)$

How does one transform a sum into a telescoping sum?

Help needed in understanding the telescoping sum for series $(a-b)\sum_{i=0}^{n-1}a^ib^{n-1-i}$.

How to prove $a^n − b^n = (a − b) \sum_{i=1}^{n}a^{n-i} b^{i-1}\le (a − b)na^{n−1}$.

Proof of Telescoping Series

Proving inequality for induction proof: $\frac1{(n+1)^2} + \frac1{n+1} < \frac1n$

Telescoping series seems not telescoping

Convergence and Divergence in $2^{-\ln n}$

Limit of a sum that seems telescopable

Computing $\frac{\sin(3)}{\cos(0)\cos(3)}+\frac{\sin(3)}{\cos(3)\cos(6)} +\cdots+\frac{\sin(3)}{\cos(42)\cos(45)}$

Find, analytically, the value of the following limit.

$S_n = \sum_{r=0}^{n-1} \cos^{-1} ( \frac{n^2+r^2+r}{\sqrt{n^4 +r^4+2r^3+2n^2r^2+2n^2r+n^2+r^2}})$ find$S_{100}$

How to find $\sum_{r=1}^{n}\frac{1}{T_r}$ when $\sum_{r=1}^{n}T_r$ is given?

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