Question

Is $\sum_{n\leq m} \exp(\delta\pi n i)$ bounded for irrational $\delta\in R$?

score 61 · Answer 1 · 2026-04-12 02:58:12

61

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Is $\sum_{n\leq m} \exp(\delta\pi n i)$ bounded for irrational $\delta\in R$?

Published on 12 Apr 2026 - 2:58

score 198 · Answer 2 · 2026-05-15 21:01:59

198

Views

Limit of $\lim\limits_{x \rightarrow \infty}{(x-\sqrt \frac{x^3+x}{x+1})}$ - calculation correct?

Published on 15 May 2026 - 21:01

score 66 · Answer 3 · 2026-04-17 00:04:23

66

Views

$1+\frac{1}{(N-1)²}+\frac{1}{(N+1)²}+\frac{1}{(2N-1)²}+\frac{1}{(2N+1)²}+...$ series

Published on 17 Apr 2026 - 0:04

score 349 · Answer 4 · 2026-04-14 04:45:38

349

Views

Prove $z^n$ converges uniformly to $0$ for $|z| < \frac 1 2$ by definition.

Published on 14 Apr 2026 - 4:45

score 103 · Answer 5 · 2026-04-12 02:48:18

103

Views

Evaluating the function $S(a) = \sum_{n=0}^{\infty} a^n \binom{2n}{n}.$

Published on 12 Apr 2026 - 2:48

score 892 · Answer 6 · 2026-05-14 19:49:28

892

Views

Sum to n terms the series $\cos \theta+ 2\cos 2\theta+ \cdots + n\cos n\theta$

Published on 14 May 2026 - 19:49

score 117 · Answer 7 · 2026-04-14 04:31:03

117

Views

Product of a decreasing sequence and a diverging series

Published on 14 Apr 2026 - 4:31

score 58 · Answer 8 · 2026-04-14 21:19:18

58

Views

A theorem on the order of summation

Published on 14 Apr 2026 - 21:19

score 271 · Answer 9 · 2026-04-29 16:16:56

271

Views

About James R. Munkres "Analysis on Manifolds" p.91 Theorem 11.1(b)

Published on 29 Apr 2026 - 16:16

score 81 · Answer 10 · 2026-04-15 03:58:14

Show that $\sum_{n=-\infty}^{\infty}\frac{e^{-i \omega_n t}}{\omega^2_n+k^2}=\frac{1}{2 k T}\left[\frac{2}{e^{k/T}-1}\cosh{k t}+e^{-k t}\right]$

score 560 · Answer 11 · 2026-05-10 18:19:54

560

Views

Calculating the Net Present Value (NPV)

Published on 10 May 2026 - 18:19

score 201 · Answer 12 · 2026-04-09 05:41:52

201

Views

Stirling type formula for Sum on $\ln(n)^2$

Published on 09 Apr 2026 - 5:41

score 58 · Answer 13 · 2026-04-09 16:05:31

58

Views

What is the distribution of the random sum?

Published on 09 Apr 2026 - 16:05

score 53 · Answer 14 · 2026-04-15 23:38:49

53

Views

Is the "term-matrix" of a $C$-finite sequence full rank?

Published on 15 Apr 2026 - 23:38

score 263 · Answer 15 · 2026-04-17 16:19:25

263

Views

If $\frac{a_1+...+a_n}{n}$ converges, $\frac{a_n}{n}\to0$, then $\frac{a_1^2+...+a_n^2}{n^2}\to 0$

Published on 17 Apr 2026 - 16:19

List Question

Is $\sum_{n\leq m} \exp(\delta\pi n i)$ bounded for irrational $\delta\in R$?

Limit of $\lim\limits_{x \rightarrow \infty}{(x-\sqrt \frac{x^3+x}{x+1})}$ - calculation correct?

$1+\frac{1}{(N-1)²}+\frac{1}{(N+1)²}+\frac{1}{(2N-1)²}+\frac{1}{(2N+1)²}+...$ series

Prove $z^n$ converges uniformly to $0$ for $|z| < \frac 1 2$ by definition.

Evaluating the function $S(a) = \sum_{n=0}^{\infty} a^n \binom{2n}{n}.$

Sum to n terms the series $\cos \theta+ 2\cos 2\theta+ \cdots + n\cos n\theta$

Product of a decreasing sequence and a diverging series

A theorem on the order of summation

About James R. Munkres "Analysis on Manifolds" p.91 Theorem 11.1(b)

Show that $\sum_{n=-\infty}^{\infty}\frac{e^{-i \omega_n t}}{\omega^2_n+k^2}=\frac{1}{2 k T}\left[\frac{2}{e^{k/T}-1}\cosh{k t}+e^{-k t}\right]$

Calculating the Net Present Value (NPV)

Stirling type formula for Sum on $\ln(n)^2$

What is the distribution of the random sum?

Is the "term-matrix" of a $C$-finite sequence full rank?

If $\frac{a_1+...+a_n}{n}$ converges, $\frac{a_n}{n}\to0$, then $\frac{a_1^2+...+a_n^2}{n^2}\to 0$

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