Question

Let $f_n(x) = \frac{x^2}{(1+x^2)^n}$ If $\sum_{n=0}^\infty$ converges pointwise, find it's limit.

score 292 · Answer 1 · 2026-04-16 16:58:44

292

Views

Let $f_n(x) = \frac{x^2}{(1+x^2)^n}$ If $\sum_{n=0}^\infty$ converges pointwise, find it's limit.

Published on 16 Apr 2026 - 16:58

score 1.2k · Answer 2 · 2026-04-14 00:45:28

1.2k

Views

Let $\{f_n\}^\infty_{n=1}$ be a sequence of continuous real valued functions defined on $\mathbb{R}$

Published on 14 Apr 2026 - 0:45

score 72 · Answer 3 · 2026-04-16 22:34:23

72

Views

Check Uniform convergence of $f_{n}\left(x\right)=\ln\left(1+\frac{1}{nx^2}\right)$ on $(0,1]$

Published on 16 Apr 2026 - 22:34

score 121 · Answer 4 · 2026-04-15 01:08:17

121

Views

Show $\int_{0}^{\infty} x^tf(x)dx$ is uniformly convergent for $t\in[a,b]$.

Published on 15 Apr 2026 - 1:08

score 188 · Answer 5 · 2026-04-13 21:56:20

188

Views

Criteria for smoothness of the pointwise limit of a sequence of functions

Published on 13 Apr 2026 - 21:56

score 585 · Answer 6 · 2026-04-14 00:03:22

585

Views

A sequence of bounded and continuous functions than converge uniformly to $f$

Published on 14 Apr 2026 - 0:03

score 152 · Answer 7 · 2026-04-14 22:05:25

152

Views

Uniform convergence of $f_{n}\left(x\right)=nxe^{-n^2x^2}$ on $0\le x<\infty $ and $ 2\le x<\infty $

Published on 14 Apr 2026 - 22:05

score 4k · Answer 8 · 2026-04-12 00:32:22

4k

Views

How to show that a series of functions does not converge uniformly?

Published on 12 Apr 2026 - 0:32

score 74 · Answer 9 · 2026-04-15 16:45:16

74

Views

Convergence uniform of $\sum _{n=1}^{\infty }\:\frac{(-1)^n}{x^2+n}$

Published on 15 Apr 2026 - 16:45

score 199 · Answer 10 · 2026-04-15 21:03:09

199

Views

Examine uniform convergence of the series $\sum_{n=1}^\infty \frac{x}{(1+(n-1)x)(1+nx)}$

Published on 15 Apr 2026 - 21:03

score 599 · Answer 11 · 2026-04-15 05:39:37

599

Views

Uniform convergence $\sum _{n=1}^{\infty }\:e^{-nx}$ on $D=[0.1,\infty)$

Published on 15 Apr 2026 - 5:39

score 122 · Answer 12 · 2026-04-16 12:04:57

122

Views

Prove that $\sum_{n=1}^\infty f_n$ converges uniformly on $\mathbb{R}$ where $f_n$ is defined piecewise.

Published on 16 Apr 2026 - 12:04

score 142 · Answer 13 · 2026-04-16 07:43:22

142

Views

Check Uniform convergence of $\sum _{n=1}^{\infty }(\frac{\ln x}{x})^n$ in $[1,\infty)$

Published on 16 Apr 2026 - 7:43

score 446 · Answer 14 · 2026-04-13 16:36:40

446

Views

Pointwise & Absolute convergence- What are ε and ?

Published on 13 Apr 2026 - 16:36

score 46 · Answer 15 · 2026-04-17 09:51:47

46

Views

Examine if $f(x) = \sum\limits_{n=1}^\infty \frac{(-1)^n}{n-x}$ is term by term differentiable

Published on 17 Apr 2026 - 9:51

List Question

Let $f_n(x) = \frac{x^2}{(1+x^2)^n}$ If $\sum_{n=0}^\infty$ converges pointwise, find it's limit.

Let $\{f_n\}^\infty_{n=1}$ be a sequence of continuous real valued functions defined on $\mathbb{R}$

Check Uniform convergence of $f_{n}\left(x\right)=\ln\left(1+\frac{1}{nx^2}\right)$ on $(0,1]$

Show $\int_{0}^{\infty} x^tf(x)dx$ is uniformly convergent for $t\in[a,b]$.

Criteria for smoothness of the pointwise limit of a sequence of functions

A sequence of bounded and continuous functions than converge uniformly to $f$

Uniform convergence of $f_{n}\left(x\right)=nxe^{-n^2x^2}$ on $0\le x<\infty $ and $ 2\le x<\infty $

How to show that a series of functions does not converge uniformly?

Convergence uniform of $\sum _{n=1}^{\infty }\:\frac{(-1)^n}{x^2+n}$

Examine uniform convergence of the series $\sum_{n=1}^\infty \frac{x}{(1+(n-1)x)(1+nx)}$

Uniform convergence $\sum _{n=1}^{\infty }\:e^{-nx}$ on $D=[0.1,\infty)$

Prove that $\sum_{n=1}^\infty f_n$ converges uniformly on $\mathbb{R}$ where $f_n$ is defined piecewise.

Check Uniform convergence of $\sum _{n=1}^{\infty }(\frac{\ln x}{x})^n$ in $[1,\infty)$

Pointwise & Absolute convergence- What are ε and ?

Examine if $f(x) = \sum\limits_{n=1}^\infty \frac{(-1)^n}{n-x}$ is term by term differentiable

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