List questions from cauchy-sequences

Published on 28 May 2018 - 23:29

513

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Solve the Cauchy Euler Equations. $x^2 y''+7x y'+13y=\ln⁡ x$

Published on 25 Mar 2026 - 6:10

752

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$\epsilon$-ball in $X$ has compact closure. Show that $X$ is complete.

Published on 30 May 2018 - 2:13

44

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Help me with analysis question on sequences.

Published on 05 Jun 2018 - 0:31

58

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look-alike Cauchy sequence

Published on 05 Jun 2018 - 5:42

859

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Proof of divergence of harmonic series with Cauchy criteria

Published on 06 Jun 2018 - 7:08

160

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The sequence $(\frac{1}{n})$ using the discrete metric is Cauchy?

Published on 10 Jun 2018 - 19:28

98

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Convergence of $\sum_{n=1}^{\infty} 3^n \sin(\frac{1}{4^nx})$

Published on 11 Jun 2018 - 12:01

819

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That a sequence is Cauchy implies it's bounded.

Published on 11 Jun 2018 - 23:46

1.2k

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Proving a sequence is bounded away from zero

Published on 12 Jun 2018 - 9:18

1.1k

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$u_{n+2}=\sqrt{u_{n+1}u_{n}}$ find limit of $\{u_n\}$

Published on 13 Jun 2018 - 17:58

3.6k

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Convergent $\implies$ Cauchy.

Published on 13 Jun 2018 - 19:17

182

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Consider the polynomial equation $x^{5}-x-1=0$

Published on 14 Jun 2018 - 1:46

123

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Completeness of $\ell^\infty$

Published on 15 Jun 2018 - 3:28

55

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Please tell me why $(y_j)$ is cofinally Cauchy?

Published on 16 Jun 2018 - 4:21

List Question

Suppose $|x_n-x_k|\le n/k^2$ for all $n$ and $k$. Show that $\{x_n\}$ is Cauchy.

Solve the Cauchy Euler Equations. $x^2 y''+7x y'+13y=\ln⁡ x$

$\epsilon$-ball in $X$ has compact closure. Show that $X$ is complete.

Help me with analysis question on sequences.

look-alike Cauchy sequence

Proof of divergence of harmonic series with Cauchy criteria

The sequence $(\frac{1}{n})$ using the discrete metric is Cauchy?

Convergence of $\sum_{n=1}^{\infty} 3^n \sin(\frac{1}{4^nx})$

That a sequence is Cauchy implies it's bounded.

Proving a sequence is bounded away from zero

$u_{n+2}=\sqrt{u_{n+1}u_{n}}$ find limit of $\{u_n\}$

Convergent $\implies$ Cauchy.

Consider the polynomial equation $x^{5}-x-1=0$

Completeness of $\ell^\infty$

Please tell me why $(y_j)$ is cofinally Cauchy?

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