Question

Prove that $\sum_{n=1}^\infty \frac{x^{2n}}{(n+x)^2}$ converges uniformly on $S=[0,1]$

score 36 · Answer 1 · 2026-04-15 17:15:26

36

Views

Prove that $\sum_{n=1}^\infty \frac{x^{2n}}{(n+x)^2}$ converges uniformly on $S=[0,1]$

Published on 15 Apr 2026 - 17:15

score 72 · Answer 2 · 2026-04-12 00:37:05

72

Views

A norm to define uniform convergence on every bounded interval.

Published on 12 Apr 2026 - 0:37

score 250 · Answer 3 · 2026-04-15 13:55:12

250

Views

Doubt on uniform convergence and sup-metric convergence

Published on 15 Apr 2026 - 13:55

score 48 · Answer 4 · 2026-04-12 21:01:50

48

Views

Propagation of Sobolev Regularity to Endpoints in Local Well-Posedness Theory

Published on 12 Apr 2026 - 21:01

score 87 · Answer 5 · 2026-04-14 12:15:23

87

Views

Is $\sum_{n=0}^{\infty}{\frac{2^{n}x^{n}}{n!}}$ convergent on $(0,1)$

Published on 14 Apr 2026 - 12:15

score 118 · Answer 6 · 2026-04-14 14:02:46

118

Views

Convergence of the sign of a function in a Sobolev space

Published on 14 Apr 2026 - 14:02

score 202 · Answer 7 · 2026-04-15 19:57:07

202

Views

Find the limit of the sequence: $x_n=\frac{1}{2\pi}\int_{0}^{\frac{\pi}{2}}\tan^{\frac{1}{n}}t \;dt$

Published on 15 Apr 2026 - 19:57

score 230 · Answer 8 · 2026-04-14 12:35:22

230

Views

counterexample sequence of continuous function converges to continuous function pointwise implies uniform convergence

Published on 14 Apr 2026 - 12:35

score 39 · Answer 9 · 2026-04-15 17:16:00

39

Views

Is $f_n=\sqrt{x^2+\frac{1}{n}}$ uniformly convergent on $D=(-\infty,+\infty)$?

Published on 15 Apr 2026 - 17:16

score 71 · Answer 10 · 2026-04-15 13:13:32

71

Views

Sequence of function which converges pointwise, is it also uniform?

Published on 15 Apr 2026 - 13:13

score 153 · Answer 11 · 2026-04-13 18:40:08

153

Views

Convergence of $\sum_{n=1}^{\infty} 1/(x-a_n)$, given that $\sum |a_n|^{-1}$ converges

Published on 13 Apr 2026 - 18:40

score 70 · Answer 12 · 2026-04-13 21:58:07

70

Views

Showing that a sequence of piecewise functions converges

Published on 13 Apr 2026 - 21:58

score 75 · Answer 13 · 2026-04-15 19:46:22

75

Views

What's the difference between $\int_{a}^{b} \lim_n f_{n}$ and $\lim_{n \to \infty} \int_{a}^{b} f_{n}$?

Published on 15 Apr 2026 - 19:46

score 109 · Answer 14 · 2026-04-16 07:43:13

109

Views

Check proof that $f_n(x)=x/n$ does not converge uniformly.

Published on 16 Apr 2026 - 7:43

score 147 · Answer 15 · 2026-04-17 08:10:17

147

Views

Proving Uniform Convergence of Sinc Function

Published on 17 Apr 2026 - 8:10

List Question

Prove that $\sum_{n=1}^\infty \frac{x^{2n}}{(n+x)^2}$ converges uniformly on $S=[0,1]$

A norm to define uniform convergence on every bounded interval.

Doubt on uniform convergence and sup-metric convergence

Propagation of Sobolev Regularity to Endpoints in Local Well-Posedness Theory

Is $\sum_{n=0}^{\infty}{\frac{2^{n}x^{n}}{n!}}$ convergent on $(0,1)$

Convergence of the sign of a function in a Sobolev space

Find the limit of the sequence: $x_n=\frac{1}{2\pi}\int_{0}^{\frac{\pi}{2}}\tan^{\frac{1}{n}}t \;dt$

counterexample sequence of continuous function converges to continuous function pointwise implies uniform convergence

Is $f_n=\sqrt{x^2+\frac{1}{n}}$ uniformly convergent on $D=(-\infty,+\infty)$?

Sequence of function which converges pointwise, is it also uniform?

Convergence of $\sum_{n=1}^{\infty} 1/(x-a_n)$, given that $\sum |a_n|^{-1}$ converges

Showing that a sequence of piecewise functions converges

What's the difference between $\int_{a}^{b} \lim_n f_{n}$ and $\lim_{n \to \infty} \int_{a}^{b} f_{n}$?

Check proof that $f_n(x)=x/n$ does not converge uniformly.

Proving Uniform Convergence of Sinc Function

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