Question

Find the values of $x$ where $\sum_n \frac{x^{2n}}{1+x^{2n}}$ converges, and show that we have a continuous function on this set

score 2.5k · Answer 1 · 2026-04-14 16:12:46

2.5k

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Find the values of $x$ where $\sum_n \frac{x^{2n}}{1+x^{2n}}$ converges, and show that we have a continuous function on this set

Published on 14 Apr 2026 - 16:12

score 1.4k · Answer 2 · 2026-04-17 01:15:32

1.4k

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Convergence of minimum of a sequence of functions

Published on 17 Apr 2026 - 1:15

score 166 · Answer 3 · 2026-04-11 19:22:38

166

Views

Asymptotically equivalent series for uniform convergence

Published on 11 Apr 2026 - 19:22

score 243 · Answer 4 · 2026-03-27 03:41:53

243

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Uniform convergence of n-fold composition using Schwarz lemma

Published on 27 Mar 2026 - 3:41

score 124 · Answer 5 · 2026-04-15 17:03:12

124

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Show that the mapping $(C^1, ||.||_{C^1}) \rightarrow (C, ||.||_\infty) $ is continuous

Published on 15 Apr 2026 - 17:03

score 40 · Answer 6 · 2026-04-12 18:06:58

40

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Function sequence and some properties

Published on 12 Apr 2026 - 18:06

score 153 · Answer 7 · 2026-04-16 01:53:01

153

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Does the series $S(x) = \sum_{n=1}^\infty \frac{n^2x^2}{n^4+x^4}$ converge uniformly?

Published on 16 Apr 2026 - 1:53

score 137 · Answer 8 · 2026-04-11 16:19:27

137

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Uniform convergence of a equicontinuous sequence of functions

Published on 11 Apr 2026 - 16:19

score 72 · Answer 9 · 2026-04-14 14:59:37

72

Views

convergence to a non-injective function

Published on 14 Apr 2026 - 14:59

score 67 · Answer 10 · 2026-04-14 20:37:39

67

Views

How can we fill in some missing details in this proof?

Published on 14 Apr 2026 - 20:37

score 917 · Answer 11 · 2026-04-14 19:18:29

917

Views

Show the uniform convergence of the partial derivatives

Published on 14 Apr 2026 - 19:18

score 64 · Answer 12 · 2026-04-15 07:02:40

64

Views

How to prove that a sequence of polygonal functions converges uniformly?

Published on 15 Apr 2026 - 7:02

score 177 · Answer 13 · 2026-04-16 16:18:07

177

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Prove the uniform convergence of $f_{1}(x)= \sqrt x , f_{n+1}(x)=\sqrt{x+f_n(x)}$ in $[0,\infty]$

Published on 16 Apr 2026 - 16:18

score 46 · Answer 14 · 2026-04-16 07:29:32

46

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Test the uniform convergence of $x^n-x^{2n}$ in $[0,1]$

Published on 16 Apr 2026 - 7:29

score 311 · Answer 15 · 2026-04-13 12:33:10

311

Views

Counterexamples in Analysis

Published on 13 Apr 2026 - 12:33

List Question

Find the values of $x$ where $\sum_n \frac{x^{2n}}{1+x^{2n}}$ converges, and show that we have a continuous function on this set

Convergence of minimum of a sequence of functions

Asymptotically equivalent series for uniform convergence

Uniform convergence of n-fold composition using Schwarz lemma

Show that the mapping $(C^1, ||.||_{C^1}) \rightarrow (C, ||.||_\infty) $ is continuous

Function sequence and some properties

Does the series $S(x) = \sum_{n=1}^\infty \frac{n^2x^2}{n^4+x^4}$ converge uniformly?

Uniform convergence of a equicontinuous sequence of functions

convergence to a non-injective function

How can we fill in some missing details in this proof?

Show the uniform convergence of the partial derivatives

How to prove that a sequence of polygonal functions converges uniformly?

Prove the uniform convergence of $f_{1}(x)= \sqrt x , f_{n+1}(x)=\sqrt{x+f_n(x)}$ in $[0,\infty]$

Test the uniform convergence of $x^n-x^{2n}$ in $[0,1]$

Counterexamples in Analysis

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