Question

proof of upper bound for a sequence convergence: $U_{n+1} =\ \frac{2\left( n^{2} +n+1\right) +nU_{n}}{( n+1)^{2}}$

score 102 · Answer 1 · 2018-11-06 11:08:54

102

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proof of upper bound for a sequence convergence: $U_{n+1} =\ \frac{2\left( n^{2} +n+1\right) +nU_{n}}{( n+1)^{2}}$

Published on 06 Nov 2018 - 11:08

score 50 · Answer 2 · 2026-03-29 20:11:32

50

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Prove that the limit as $y$ goes to $0$ of $V(x,y)=F(x)$ if $V(x,y)=\frac{1}{\pi}\int^{\infty}_{-\infty}\frac{yF(\lambda)}{y^2+(\lambda-x)^2}d\lambda$

Published on 29 Mar 2026 - 20:11

score 103 · Answer 3 · 2026-03-29 07:19:50

103

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How to test the uniform convergence of a function series, without Weierstrass M-test

Published on 29 Mar 2026 - 7:19

score 222 · Answer 4 · 2018-11-06 22:20:44

222

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Convergence of a sequence of partial sums of partial sums

Published on 06 Nov 2018 - 22:20

score 124 · Answer 5 · 2018-11-07 00:57:26

124

Views

example of a sequence with no convergent subsequence

Published on 07 Nov 2018 - 0:57

score 173 · Answer 6 · 2018-11-07 06:08:20

173

Views

Arithmetic Mean of Partial Sums of Geometric Series

Published on 07 Nov 2018 - 6:08

score 1.3k · Answer 7 · 2018-11-07 14:11:47

1.3k

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Let $E$ be a subset of $\mathbb{R}^k$. Show that $E$ is compact if and only if every sequence in $E$ has a converging subsequence to a point in $E$.

Published on 07 Nov 2018 - 14:11

score 500 · Answer 8 · 2026-04-04 15:46:48

500

Views

Appropriate number of significant figures to use in plot

Published on 04 Apr 2026 - 15:46

score 70 · Answer 9 · 2018-11-07 19:28:47

70

Views

About the pointwise convergence of a series

Published on 07 Nov 2018 - 19:28

score 52 · Answer 10 · 2026-03-27 14:58:22

52

Views

Show that $||e^{-\lambda k}x-x||\to0$ as $\lambda\to0$ when $x = \{x_k\}_k \in \ell^2$

Published on 27 Mar 2026 - 14:58

score 90 · Answer 11 · 2026-03-29 20:44:35

90

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Show that $F = \{\lambda x|\lambda\in \mathbb{R}_+, x\in K\}$ is closed where $K$ is a compact set.

Published on 29 Mar 2026 - 20:44

score 66 · Answer 12 · 2026-03-22 19:27:19

66

Views

Preserving Bijectivity under pointwise limit

Published on 22 Mar 2026 - 19:27

score 1k · Answer 13 · 2026-03-29 20:38:50

1k

Views

Rudin's Proof of Bolzano-Weierstrass theorem

Published on 29 Mar 2026 - 20:38

score 139 · Answer 14 · 2026-03-25 07:48:52

139

Views

Is the algebra map of the ultrafilter monad continuous?

Published on 25 Mar 2026 - 7:48

score 665 · Answer 15 · 2026-03-28 09:57:12

665

Views

What is this sum equal to? $\sigma(n)=\sum_{i\neq j} \frac{1}{i^n j^n}$

Published on 28 Mar 2026 - 9:57

List Question

proof of upper bound for a sequence convergence: $U_{n+1} =\ \frac{2\left( n^{2} +n+1\right) +nU_{n}}{( n+1)^{2}}$

Prove that the limit as $y$ goes to $0$ of $V(x,y)=F(x)$ if $V(x,y)=\frac{1}{\pi}\int^{\infty}_{-\infty}\frac{yF(\lambda)}{y^2+(\lambda-x)^2}d\lambda$

How to test the uniform convergence of a function series, without Weierstrass M-test

Convergence of a sequence of partial sums of partial sums

example of a sequence with no convergent subsequence

Arithmetic Mean of Partial Sums of Geometric Series

Let $E$ be a subset of $\mathbb{R}^k$. Show that $E$ is compact if and only if every sequence in $E$ has a converging subsequence to a point in $E$.

Appropriate number of significant figures to use in plot

About the pointwise convergence of a series

Show that $||e^{-\lambda k}x-x||\to0$ as $\lambda\to0$ when $x = \{x_k\}_k \in \ell^2$

Show that $F = \{\lambda x|\lambda\in \mathbb{R}_+, x\in K\}$ is closed where $K$ is a compact set.

Preserving Bijectivity under pointwise limit

Rudin's Proof of Bolzano-Weierstrass theorem

Is the algebra map of the ultrafilter monad continuous?

What is this sum equal to? $\sigma(n)=\sum_{i\neq j} \frac{1}{i^n j^n}$

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