List questions from cauchy-sequences

Published on 13 Dec 2019 - 17:12

171

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$|x_{n+1} - x_n | \le C|x_n - x_{n-1}|$ (show that $x_n$ is Cauchy)

Published on 15 Dec 2019 - 22:53

192

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Prove that Weierstrass-like function is not differentiable

Published on 22 Dec 2019 - 0:54

1.7k

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How to show a metric space is not complete

Published on 26 Mar 2026 - 10:59

27

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Functional form of convergent infinite geometric series

Published on 03 Jan 2020 - 1:24

72

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Prove that sequence it's a Cauchy Sequence ( $\mid a_{n+1}-a_n \mid\leq \frac{1}{n^2}$ )

Published on 03 Jan 2020 - 17:49

68

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If $e^{iux_n}$ converges for $u\in\mathbb{R}$, $x_n$ converge to a finite limit

Published on 11 Jan 2020 - 9:17

108

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Question on Condition for a Normed Space to be Banach

Published on 18 Jan 2020 - 15:45

49

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Help with proofs

Published on 21 Jan 2020 - 21:01

252

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Questions about proof for metric space completion

Published on 26 Mar 2026 - 11:06

76

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Integrals of $L^1$-Cauchy-Sequence which converges to zero almost everywhere converges to zero

Published on 22 Jan 2020 - 16:40

86

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Why is $|S_{m}-S_{n}|$ a Cauchy sequence in Weierstrass’ M-test?

Published on 24 Feb 2026 - 2:11

95

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How do I disprove uniform continuity in this particular case?

Published on 23 Jan 2020 - 15:22

87

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Show $\{x_n\}$ where $x_n = \frac{n}{n+1}$ is Cauchy

Published on 24 Jan 2020 - 2:27

28

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How to prove this involving sequences

Published on 24 Jan 2020 - 19:51

List Question

Heron's Method: prove convergence in $\mathbb{Q}$.

$|x_{n+1} - x_n | \le C|x_n - x_{n-1}|$ (show that $x_n$ is Cauchy)

Prove that Weierstrass-like function is not differentiable

How to show a metric space is not complete

Functional form of convergent infinite geometric series

Prove that sequence it's a Cauchy Sequence ( $\mid a_{n+1}-a_n \mid\leq \frac{1}{n^2}$ )

If $e^{iux_n}$ converges for $u\in\mathbb{R}$, $x_n$ converge to a finite limit

Question on Condition for a Normed Space to be Banach

Help with proofs

Questions about proof for metric space completion

Integrals of $L^1$-Cauchy-Sequence which converges to zero almost everywhere converges to zero

Why is $|S_{m}-S_{n}|$ a Cauchy sequence in Weierstrass’ M-test?

How do I disprove uniform continuity in this particular case?

Show $\{x_n\}$ where $x_n = \frac{n}{n+1}$ is Cauchy

How to prove this involving sequences

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