Question

Does the sum $\sum\limits^{\infty}_{k=1} \frac{\sin(kx)}{k^{\alpha}}$ converge for $\alpha > \frac{1}{2}$ and $x \in [0,2 \pi]$?

score 2.8k · Answer 1 · 2013-12-28 20:49:10

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Does the sum $\sum\limits^{\infty}_{k=1} \frac{\sin(kx)}{k^{\alpha}}$ converge for $\alpha > \frac{1}{2}$ and $x \in [0,2 \pi]$?

Published on 28 Dec 2013 - 20:49

score 1k · Answer 2 · 2014-01-02 17:30:00

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Prove $ \cos\left(\frac{2\pi}{5}\right) + \cos\left(\frac{4\pi}{5}\right) + \cos\left(\frac{6\pi}{5}\right)+ \cos\left(\frac{8\pi}{5}\right) = -1 $

Published on 02 Jan 2014 - 17:30

score 2.7k · Answer 3 · 2014-01-09 09:48:03

2.7k

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Does the series $\sum_{n\ge1}\left(-1\right)^n\frac{\cos\left(\alpha n\right)} {\sqrt n}$ converge?

Published on 09 Jan 2014 - 9:48

score 221 · Answer 4 · 2014-01-19 07:32:12

221

Views

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score 225 · Answer 5 · 2026-03-26 18:50:29

225

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score 1.2k · Answer 6 · 2014-02-10 10:37:35

1.2k

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score 139 · Answer 7 · 2026-03-25 17:36:33

139

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score 147 · Answer 8 · 2014-02-12 16:51:32

147

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How to prove that $\Sigma_{n=1}^{N-1}{\sin^2\frac{p\pi{}n}{N}} = \frac{N}{2}$

Published on 12 Feb 2014 - 16:51

score 74 · Answer 9 · 2026-03-26 12:34:38

74

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Series representation of $\sin(nu)$ when $n$ is an odd integer?

Published on 26 Mar 2026 - 12:34

score 174 · Answer 10 · 2026-02-23 03:49:21

174

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Evaluating $\int_0^{\frac{\pi}2}\frac{\sin 2x}{\sqrt{x}}\,dx$

Published on 23 Feb 2026 - 3:49

score 2.9k · Answer 11 · 2014-03-06 21:47:09

2.9k

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score 37 · Answer 12 · 2014-03-08 20:27:33

37

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score 107 · Answer 13 · 2014-03-10 11:02:55

107

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Published on 10 Mar 2014 - 11:02

score 702 · Answer 14 · 2017-04-11 13:59:00

702

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Published on 11 Apr 2017 - 13:59

score 537 · Answer 15 · 2017-04-12 11:38:12

537

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List Question

Does the sum $\sum\limits^{\infty}_{k=1} \frac{\sin(kx)}{k^{\alpha}}$ converge for $\alpha > \frac{1}{2}$ and $x \in [0,2 \pi]$?

Prove $ \cos\left(\frac{2\pi}{5}\right) + \cos\left(\frac{4\pi}{5}\right) + \cos\left(\frac{6\pi}{5}\right)+ \cos\left(\frac{8\pi}{5}\right) = -1 $

Does the series $\sum_{n\ge1}\left(-1\right)^n\frac{\cos\left(\alpha n\right)} {\sqrt n}$ converge?

Closed form for a trigonometric partial sum

Convergence of Trigonometric Dirichlet series

Proof that the sum $\sum _{n=1} ^{\infty} (-1)^n \sin (nx)$ is bounded

converting a signal back and forth with trigonometric functions

How to prove that $\Sigma_{n=1}^{N-1}{\sin^2\frac{p\pi{}n}{N}} = \frac{N}{2}$

Series representation of $\sin(nu)$ when $n$ is an odd integer?

Evaluating $\int_0^{\frac{\pi}2}\frac{\sin 2x}{\sqrt{x}}\,dx$

How do I find the direction angle of a vector?

Integrating Trigonometric Series

What is the pupose of using minute and seconds with degree?

Convergence of $\sum \frac{\sin(n^2)}{n}$

Relationship Between Sine as a Series and Sine in Triangles

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