Question

For which $p$ does $ \sum_{n=2}^{\infty} \frac{\sin(\frac{\pi}{n})}{n^p}$ converge?

score 160 · Answer 1 · 2019-02-08 17:12:59

160

Views

For which $p$ does $ \sum_{n=2}^{\infty} \frac{\sin(\frac{\pi}{n})}{n^p}$ converge?

Published on 08 Feb 2019 - 17:12

score 36 · Answer 2 · 2026-03-25 01:27:59

36

Views

How to show $\int_{0}^{1}|f|^{p}|g_{n}-g|^pd\mu$

Published on 25 Mar 2026 - 1:27

score 453 · Answer 3 · 2019-02-08 18:24:02

453

Views

Assume $\sum a_k$ is a series of positive terms that converges. Prove that $\sum \frac1{a_k}$ is divergent

Published on 08 Feb 2019 - 18:24

score 69 · Answer 4 · 2019-02-08 20:17:43

69

Views

Does $\lim_{x\to 0} \frac {f(x)}{|x|} \leq M $ ,for some real $M$ ,imply that $f(x)\leq |x| M $?

Published on 08 Feb 2019 - 20:17

score 1.1k · Answer 5 · 2019-02-08 20:30:21

1.1k

Views

Show directly that if $\{s_n\}$ is a Cauchy sequence then so is $\{|s_n|\}$. Conclude that $\{|s_n|\}$ converges whenever $\{s_n\}$ converges.

Published on 08 Feb 2019 - 20:30

score 358 · Answer 6 · 2026-04-09 02:24:24

358

Views

Uniform convergence in $\sup$ and $\inf$ convolutions

Published on 09 Apr 2026 - 2:24

score 513 · Answer 7 · 2019-02-08 22:12:14

513

Views

Show that recursive sequence is decreasing

Published on 08 Feb 2019 - 22:12

score 81 · Answer 8 · 2026-04-11 20:46:23

81

Views

Show that sequence is Cauchy

Published on 11 Apr 2026 - 20:46

score 1.4k · Answer 9 · 2019-02-09 03:59:00

1.4k

Views

Prove that the sequence $f(n)$ = $(1/(n)^{0.5}) ,∀n ∈ N $converges towards 0.

Published on 09 Feb 2019 - 3:59

score 34 · Answer 10 · 2026-04-11 07:24:48

34

Views

Am I going about testing for convergence correctly for this example?

Published on 11 Apr 2026 - 7:24

score 85 · Answer 11 · 2019-02-10 04:20:38

85

Views

Convergence to arithmetic mean of the following series

Published on 10 Feb 2019 - 4:20

score 297 · Answer 12 · 2026-04-09 03:37:06

297

Views

How would you manipulate this series to use the alternating series test?

Published on 09 Apr 2026 - 3:37

score 81 · Answer 13 · 2019-02-10 15:50:05

81

Views

Convergence of subsequences and adherent values

Published on 10 Feb 2019 - 15:50

score 122 · Answer 14 · 2019-02-10 16:52:10

122

Views

Show, that the sequence $ a_n = \left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{9}\right)\cdot\ldots\cdot\left(1+\frac{1}{3^n}\right) $ converges.

Published on 10 Feb 2019 - 16:52

score 120 · Answer 15 · 2026-04-12 15:52:07

120

Views

Does product of $L^1$ convergent martingales converge?

Published on 12 Apr 2026 - 15:52

List Question

For which $p$ does $ \sum_{n=2}^{\infty} \frac{\sin(\frac{\pi}{n})}{n^p}$ converge?

How to show $\int_{0}^{1}|f|^{p}|g_{n}-g|^pd\mu$

Assume $\sum a_k$ is a series of positive terms that converges. Prove that $\sum \frac1{a_k}$ is divergent

Does $\lim_{x\to 0} \frac {f(x)}{|x|} \leq M $ ,for some real $M$ ,imply that $f(x)\leq |x| M $?

Show directly that if $\{s_n\}$ is a Cauchy sequence then so is $\{|s_n|\}$. Conclude that $\{|s_n|\}$ converges whenever $\{s_n\}$ converges.

Uniform convergence in $\sup$ and $\inf$ convolutions

Show that recursive sequence is decreasing

Show that sequence is Cauchy

Prove that the sequence $f(n)$ = $(1/(n)^{0.5}) ,∀n ∈ N $converges towards 0.

Am I going about testing for convergence correctly for this example?

Convergence to arithmetic mean of the following series

How would you manipulate this series to use the alternating series test?

Convergence of subsequences and adherent values

Show, that the sequence $ a_n = \left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{9}\right)\cdot\ldots\cdot\left(1+\frac{1}{3^n}\right) $ converges.

Does product of $L^1$ convergent martingales converge?

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