Question

Can I find the sum of a series by the use of differentiation and limits?

score 74 · Answer 1 · 2026-04-11 05:37:06

74

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Can I find the sum of a series by the use of differentiation and limits?

Published on 11 Apr 2026 - 5:37

score 166 · Answer 2 · 2026-04-11 23:42:43

166

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Converse of theorem on differentiating term by term

Published on 11 Apr 2026 - 23:42

score 49 · Answer 3 · 2026-04-16 17:20:54

49

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$f\in L^1_{\text{bc}}\left(\mathbb R\right)$ and $x^2f\left(x\right)$ bounded $\implies$ $\sum_{k\in\mathbb Z}f\left(x+k\right)$ uniformly convergent

Published on 16 Apr 2026 - 17:20

score 469 · Answer 4 · 2026-04-16 17:36:48

469

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Uniform Convergence of $f_n(x)= \cos^nx(1-\cos^nx)$

Published on 16 Apr 2026 - 17:36

score 2k · Answer 5 · 2026-04-14 17:41:36

2k

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Uniform Convergence and LimSup's

Published on 14 Apr 2026 - 17:41

score 649 · Answer 6 · 2026-04-14 05:24:44

649

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Uniform convergence of integral.

Published on 14 Apr 2026 - 5:24

score 46 · Answer 7 · 2026-04-11 02:28:04

46

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What is the reason that the series of derivavtives does not converge uniformly.

Published on 11 Apr 2026 - 2:28

score 243 · Answer 8 · 2026-04-15 18:40:11

243

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Examine the uniform convergence of the series of functions $f_n: \mathbb{R} \to \mathbb{R}: x \mapsto \frac{(-1)^n}{n}$

Published on 15 Apr 2026 - 18:40

score 418 · Answer 9 · 2026-04-16 02:20:25

418

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Examine uniform convergence of the series of functions with $f_n: [1,2] \to \mathbb{R}: x \mapsto xe^{-nx}$

Published on 16 Apr 2026 - 2:20

score 81 · Answer 10 · 2026-04-14 17:10:14

81

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Showing the series $\sum_{n=1}^{\infty}(-1)^n\frac{x^2+n}{n^2}$ is uniformly convergent in any bounded interval.

Published on 14 Apr 2026 - 17:10

score 1.3k · Answer 11 · 2026-04-15 11:09:55

1.3k

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Show that a series of functions converges (uniformly)

Published on 15 Apr 2026 - 11:09

score 123 · Answer 12 · 2026-04-16 00:46:00

123

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For function $f(x)=\sum_{n=1}^{\infty}\frac{n[nx]}{4^n}$, prove or disprove that $\int_{-1}^1f(x)dx$ is a rational number.

Published on 16 Apr 2026 - 0:46

score 81 · Answer 13 · 2026-04-15 08:03:16

81

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Discuss the convergence and the uniform convergence of a series

Published on 15 Apr 2026 - 8:03

score 1.1k · Answer 14 · 2026-03-29 06:28:48

1.1k

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Convergence of characteristic function $\chi_{(n,\infty)}$

Published on 29 Mar 2026 - 6:28

score 226 · Answer 15 · 2026-04-16 02:40:11

226

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the sequence $\{f_n\}$ is uniformly convergent

Published on 16 Apr 2026 - 2:40

List Question

Can I find the sum of a series by the use of differentiation and limits?

Converse of theorem on differentiating term by term

$f\in L^1_{\text{bc}}\left(\mathbb R\right)$ and $x^2f\left(x\right)$ bounded $\implies$ $\sum_{k\in\mathbb Z}f\left(x+k\right)$ uniformly convergent

Uniform Convergence of $f_n(x)= \cos^nx(1-\cos^nx)$

Uniform Convergence and LimSup's

Uniform convergence of integral.

What is the reason that the series of derivavtives does not converge uniformly.

Examine the uniform convergence of the series of functions $f_n: \mathbb{R} \to \mathbb{R}: x \mapsto \frac{(-1)^n}{n}$

Examine uniform convergence of the series of functions with $f_n: [1,2] \to \mathbb{R}: x \mapsto xe^{-nx}$

Showing the series $\sum_{n=1}^{\infty}(-1)^n\frac{x^2+n}{n^2}$ is uniformly convergent in any bounded interval.

Show that a series of functions converges (uniformly)

For function $f(x)=\sum_{n=1}^{\infty}\frac{n[nx]}{4^n}$, prove or disprove that $\int_{-1}^1f(x)dx$ is a rational number.

Discuss the convergence and the uniform convergence of a series

Convergence of characteristic function $\chi_{(n,\infty)}$

the sequence $\{f_n\}$ is uniformly convergent

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