Question

Prove that $\sum_{n=1}^{\infty} \frac{(-1)^{[\sqrt n]}}{n}$ is converges where $[x]$ is the largest integer is less than or equal to x.

score 76 · Answer 1 · 2019-12-09 17:10:00

76

Views

Prove that $\sum_{n=1}^{\infty} \frac{(-1)^{[\sqrt n]}}{n}$ is converges where $[x]$ is the largest integer is less than or equal to x.

Published on 09 Dec 2019 - 17:10

score 174 · Answer 2 · 2019-12-09 20:40:10

174

Views

Uniform Convergence using Dirichlet's Test

Published on 09 Dec 2019 - 20:40

score 320 · Answer 3 · 2026-03-29 14:19:59

320

Views

Inner product spaces, orthogonality, complex integration and non-uniform convergence

Published on 29 Mar 2026 - 14:19

score 109 · Answer 4 · 2019-12-10 11:13:26

109

Views

Uniform convergence of $\sum_{k=1}^{\infty} \frac{1}{k}\arctan(\frac{x}{k})$ on $\mathbb{R}$

Published on 10 Dec 2019 - 11:13

score 29 · Answer 5 · 2019-12-10 14:00:33

29

Views

Interval for uniform convergence

Published on 10 Dec 2019 - 14:00

score 458 · Answer 6 · 2026-03-25 10:57:16

458

Views

Convergence of Lipschitz functions in $L^\infty$ implies the convergence in $H^{1}$

Published on 25 Mar 2026 - 10:57

score 87 · Answer 7 · 2019-12-10 22:36:46

87

Views

Proof of $x^n(1-x)$ uniformly converges to $0$ on $[0,1]$

Published on 10 Dec 2019 - 22:36

score 50 · Answer 8 · 2019-12-11 11:52:42

50

Views

Uniform convergence help

Published on 11 Dec 2019 - 11:52

score 40 · Answer 9 · 2026-03-25 06:06:17

40

Views

Show that $\theta(z)=\sum_{m=-\infty}^{\infty}e^{-\pi m^2z}$ converges and is analytic in $z\in \mathbb C,Re(z)>0$

Published on 25 Mar 2026 - 6:06

score 56 · Answer 10 · 2019-12-12 17:48:57

56

Views

Convergence, continuity, differentiability of an improper integral

Published on 12 Dec 2019 - 17:48

score 561 · Answer 11 · 2026-02-23 08:28:36

561

Views

Pointwise convergent, increasing sequence

Published on 23 Feb 2026 - 8:28

score 107 · Answer 12 · 2019-12-13 01:08:23

107

Views

Show that $\sum_{n=1}^{\infty}\frac{sin(x^{n})}{n!}$ converges uniformly for $x \in \mathbb R$.

Published on 13 Dec 2019 - 1:08

score 56 · Answer 13 · 2026-02-24 00:47:23

56

Views

proving uniform convergence of function series from pointwise convergence

Published on 24 Feb 2026 - 0:47

score 38 · Answer 14 · 2026-04-03 19:44:06

38

Views

Calculate Fourier series and prove uniform convergence

Published on 03 Apr 2026 - 19:44

score 89 · Answer 15 · 2019-12-15 04:40:37

89

Views

If $f_n\to f$ uniformly and $\lim_{x \to \infty}f_n(x)=0$ for all $n$. Then $\lim_{x \to \infty}f(x)=0$

Published on 15 Dec 2019 - 4:40

List Question

Prove that $\sum_{n=1}^{\infty} \frac{(-1)^{[\sqrt n]}}{n}$ is converges where $[x]$ is the largest integer is less than or equal to x.

Uniform Convergence using Dirichlet's Test

Inner product spaces, orthogonality, complex integration and non-uniform convergence

Uniform convergence of $\sum_{k=1}^{\infty} \frac{1}{k}\arctan(\frac{x}{k})$ on $\mathbb{R}$

Interval for uniform convergence

Convergence of Lipschitz functions in $L^\infty$ implies the convergence in $H^{1}$

Proof of $x^n(1-x)$ uniformly converges to $0$ on $[0,1]$

Uniform convergence help

Show that $\theta(z)=\sum_{m=-\infty}^{\infty}e^{-\pi m^2z}$ converges and is analytic in $z\in \mathbb C,Re(z)>0$

Convergence, continuity, differentiability of an improper integral

Pointwise convergent, increasing sequence

Show that $\sum_{n=1}^{\infty}\frac{sin(x^{n})}{n!}$ converges uniformly for $x \in \mathbb R$.

proving uniform convergence of function series from pointwise convergence

Calculate Fourier series and prove uniform convergence

If $f_n\to f$ uniformly and $\lim_{x \to \infty}f_n(x)=0$ for all $n$. Then $\lim_{x \to \infty}f(x)=0$

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