Question

How to formally show that following summation is equivalent?

score 29 · Answer 1 · 2018-05-18 03:45:16

29

Views

How to formally show that following summation is equivalent?

Published on 18 May 2018 - 3:45

score 98 · Answer 2 · 2018-05-18 05:55:04

98

Views

How to evaluate $\sum_{k=2}^\infty (11k + 7)(k+1)\frac{M^{2k+1}}{(M+N)^{2k+4}}$ as a integral?

Published on 18 May 2018 - 5:55

score 95 · Answer 3 · 2018-05-18 11:51:39

95

Views

How do I prove that $\sum_{i=1}^m \cos^2\left(\frac{2\pi i}{m}\right) = \sum_{i=1}^m \sin^2\left(\frac{2\pi i}{m}\right) = \frac{m}{2}$?

Published on 18 May 2018 - 11:51

score 605 · Answer 4 · 2018-05-18 11:55:44

605

Views

If $(X_n)$ are i.i.d random variables, then $P(X_1\geq 0)=1$ and $P(X_1 >0)>0$ implies $\sum X_n =\infty$

Published on 18 May 2018 - 11:55

score 60 · Answer 5 · 2026-03-25 06:00:28

60

Views

Summation series question divergent inequality

Published on 25 Mar 2026 - 6:00

score 786 · Answer 6 · 2026-03-25 01:18:50

786

Views

Summation of $\sum_{r=1}^{n} \frac{\cos (2rx)}{\sin((2r+1)x \sin((2r-1)x}$

Published on 25 Mar 2026 - 1:18

score 277 · Answer 7 · 2018-05-19 11:36:12

277

Views

Evaluating $\sum_{n=1}^{N} 2^{-n}\sin(n\theta)$

Published on 19 May 2018 - 11:36

score 55 · Answer 8 · 2026-03-25 19:25:20

55

Views

Find the primitive function of $\sum_{n=1}^{\infty}\frac{(-1)^n(2n+2)}{n!}(x-1)^{2n+1}$

Published on 25 Mar 2026 - 19:25

score 52 · Answer 9 · 2026-03-25 17:20:05

52

Views

Can $- (s^2 + (n + 1) s + n (n - 1)) \frac{\prod^{n - 2}_{^{} k = 1} (s - k)}{\prod^n_{k = 0} (s + k)}$ be written as a hypergeometric function?

Published on 25 Mar 2026 - 17:20

score 242 · Answer 10 · 2026-03-25 06:04:01

242

Views

Are $(2,28)$ and $(5,3207)$ the only solutions $(m,n)\in\mathbb{N}^2$?

Published on 25 Mar 2026 - 6:04

score 69 · Answer 11 · 2026-03-24 23:42:30

69

Views

Telescopic Product involving Complex Numbers

Published on 24 Mar 2026 - 23:42

score 31 · Answer 12 · 2018-05-20 15:16:43

31

Views

Geometric series summation

Published on 20 May 2018 - 15:16

score 190 · Answer 13 · 2018-05-20 18:32:14

190

Views

Evaluate $\lim_{n \to \infty} \sum_{k=n}^{2n} \frac{1}{n+\sqrt{k}}$

Published on 20 May 2018 - 18:32

score 72 · Answer 14 · 2026-03-26 16:05:16

72

Views

Convergence of an infinite sum involving Gauss' hypergeometric function

Published on 26 Mar 2026 - 16:05

score 77 · Answer 15 · 2026-03-25 19:17:40

77

Views

Inequality with a condition

Published on 25 Mar 2026 - 19:17

List Question

How to formally show that following summation is equivalent?

How to evaluate $\sum_{k=2}^\infty (11k + 7)(k+1)\frac{M^{2k+1}}{(M+N)^{2k+4}}$ as a integral?

How do I prove that $\sum_{i=1}^m \cos^2\left(\frac{2\pi i}{m}\right) = \sum_{i=1}^m \sin^2\left(\frac{2\pi i}{m}\right) = \frac{m}{2}$?

If $(X_n)$ are i.i.d random variables, then $P(X_1\geq 0)=1$ and $P(X_1 >0)>0$ implies $\sum X_n =\infty$

Summation series question divergent inequality

Summation of $\sum_{r=1}^{n} \frac{\cos (2rx)}{\sin((2r+1)x \sin((2r-1)x}$

Evaluating $\sum_{n=1}^{N} 2^{-n}\sin(n\theta)$

Find the primitive function of $\sum_{n=1}^{\infty}\frac{(-1)^n(2n+2)}{n!}(x-1)^{2n+1}$

Can $- (s^2 + (n + 1) s + n (n - 1)) \frac{\prod^{n - 2}_{^{} k = 1} (s - k)}{\prod^n_{k = 0} (s + k)}$ be written as a hypergeometric function?

Are $(2,28)$ and $(5,3207)$ the only solutions $(m,n)\in\mathbb{N}^2$?

Telescopic Product involving Complex Numbers

Geometric series summation

Evaluate $\lim_{n \to \infty} \sum_{k=n}^{2n} \frac{1}{n+\sqrt{k}}$

Convergence of an infinite sum involving Gauss' hypergeometric function

Inequality with a condition

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