Question

How does one show that an alternating series $\sum_{n=1}^{\infty}\frac{\sin^2(n)}{2n}$ is unbounded/diverges?

score 52 · Answer 1 · 2024-03-08 20:45:54

52

Views

How does one show that an alternating series $\sum_{n=1}^{\infty}\frac{\sin^2(n)}{2n}$ is unbounded/diverges?

Published on 08 Mar 2024 - 20:45

score 112 · Answer 2 · 2024-03-09 16:36:18

112

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Limit $\lim_{n\to +\infty}{\frac{\left(n!\right)^2\cdot4^n\cdot n}{\left(2n\right)!}}$

Published on 09 Mar 2024 - 16:36

score 21 · Answer 3 · 2024-03-13 02:18:22

21

Views

How to construct a complex function series that converges uniformly on a closed region but its derivative does not converge uniformly on the boundary?

Published on 13 Mar 2024 - 2:18

score 93 · Answer 4 · 2024-03-14 12:31:13

93

Views

Are Caesaro summation and Abelian summation frown upon in mathematical community?

Published on 14 Mar 2024 - 12:31

score 21 · Answer 5 · 2024-03-16 19:17:24

21

Views

Infinite series involving Lambert W function

Published on 16 Mar 2024 - 19:17

score 63 · Answer 6 · 2024-03-20 11:46:39

63

Views

Showing divergence of $\sum\limits_{k=1}^{\infty} \log\left(1+\frac{(-1)^{k+1}}{k^\alpha}\right)$ where $0<\alpha<\frac{1}{2}$

Published on 20 Mar 2024 - 11:46

score 79 · Answer 7 · 2026-03-26 19:01:53

79

Views

How to find the divergent renormalization of $\sum_{n=1}^{\infty} \frac{2^n}{n}$?

Published on 26 Mar 2026 - 19:01

score 66 · Answer 8 · 2015-01-03 14:26:46

66

Views

Show that this sum is divergent

Published on 03 Jan 2015 - 14:26

score 11.1k · Answer 9 · 2015-01-03 15:29:23

11.1k

Views

Does $\sum\limits_n \log\left(1+{1\over n}\right)$ diverge or converge?

Published on 03 Jan 2015 - 15:29

score 126 · Answer 10 · 2015-01-03 16:06:29

126

Views

Series convergence - factorial over products

Published on 03 Jan 2015 - 16:06

score 36 · Answer 11 · 2015-01-04 08:14:41

36

Views

Divergence proof problem in introductory analysis text.

Published on 04 Jan 2015 - 8:14

score 300 · Answer 12 · 2015-01-04 14:58:42

300

Views

Convergence of series for specific values of $\lambda$.

Published on 04 Jan 2015 - 14:58

score 364 · Answer 13 · 2015-01-05 02:43:16

364

Views

$\sum_{n=0}^{\infty} \frac{1}{2n+1} = 0.66215 + \frac{1}{2}\log(\infty)^{3}$

Published on 05 Jan 2015 - 2:43

score 52 · Answer 14 · 2015-01-06 08:34:20

52

Views

check the convergence of the series

Published on 06 Jan 2015 - 8:34

score 99 · Answer 15 · 2015-01-06 10:27:53

99

Views

convergence of $\sum_{n=1}^{\infty}(\sqrt{n^2+7}-\sqrt[3]{n^3+8n+1})\ln(1+1/n)$

Published on 06 Jan 2015 - 10:27

List Question

How does one show that an alternating series $\sum_{n=1}^{\infty}\frac{\sin^2(n)}{2n}$ is unbounded/diverges?

Limit $\lim_{n\to +\infty}{\frac{\left(n!\right)^2\cdot4^n\cdot n}{\left(2n\right)!}}$

How to construct a complex function series that converges uniformly on a closed region but its derivative does not converge uniformly on the boundary?

Are Caesaro summation and Abelian summation frown upon in mathematical community?

Infinite series involving Lambert W function

Showing divergence of $\sum\limits_{k=1}^{\infty} \log\left(1+\frac{(-1)^{k+1}}{k^\alpha}\right)$ where $0<\alpha<\frac{1}{2}$

How to find the divergent renormalization of $\sum_{n=1}^{\infty} \frac{2^n}{n}$?

Show that this sum is divergent

Does $\sum\limits_n \log\left(1+{1\over n}\right)$ diverge or converge?

Series convergence - factorial over products

Divergence proof problem in introductory analysis text.

Convergence of series for specific values of $\lambda$.

$\sum_{n=0}^{\infty} \frac{1}{2n+1} = 0.66215 + \frac{1}{2}\log(\infty)^{3}$

check the convergence of the series

convergence of $\sum_{n=1}^{\infty}(\sqrt{n^2+7}-\sqrt[3]{n^3+8n+1})\ln(1+1/n)$

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