Question

If $A \subset \mathbb{R}^n$ is bounded an open then every sequence of $A$ has a subsequence that converges to a point of $A$

score 56 · Answer 1 · 2018-09-05 20:44:18

56

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If $A \subset \mathbb{R}^n$ is bounded an open then every sequence of $A$ has a subsequence that converges to a point of $A$

Published on 05 Sep 2018 - 20:44

score 829 · Answer 2 · 2026-04-02 21:00:31

829

Views

Every convergent sequence $(x_n)$ is bounded in $(M,d)$

Published on 02 Apr 2026 - 21:00

score 39 · Answer 3 · 2026-03-28 02:24:26

39

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If $f(x)=\sum^{\infty}_{n=0}a_n x^n$ converges for $x=50$, can $f$ be uniformly continuous over $[0,10]$?

Published on 28 Mar 2026 - 2:24

score 1k · Answer 4 · 2018-09-06 02:39:06

1k

Views

If ${a_n}$ converges, then ${a_{2n}}$ converges proof question

Published on 06 Sep 2018 - 2:39

score 236 · Answer 5 · 2018-09-06 06:05:08

236

Views

Let $\{a_n\}$ be a decreasing sequence of positive real numbers converging to $0,$ then $\sum^{\infty}_{n=1}(-1)^{n}a_n$ converges

Published on 06 Sep 2018 - 6:05

score 1.3k · Answer 6 · 2018-09-06 10:15:53

1.3k

Views

Lagrange’s Remainder Theorem

Published on 06 Sep 2018 - 10:15

score 77 · Answer 7 · 2018-09-06 11:52:42

77

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Convergence of $\sum_{n=1}^{\infty}(-n)^{\lfloor\alpha\rfloor}\frac{\sin^3\left(\frac{1}{n}\right)}{\left(\log(n)\right)^{\alpha-1}}$

Published on 06 Sep 2018 - 11:52

score 576 · Answer 8 · 2018-09-06 19:50:31

576

Views

finding limit of a sequence of vectors

Published on 06 Sep 2018 - 19:50

score 48 · Answer 9 · 2026-03-25 18:59:48

48

Views

Easy Lim Sup Proof?

Published on 25 Mar 2026 - 18:59

score 47 · Answer 10 · 2026-03-25 06:07:14

47

Views

Convergence of expectations of product of r.v.

Published on 25 Mar 2026 - 6:07

score 63 · Answer 11 · 2018-09-07 00:13:55

63

Views

If $\{b_{n}\}$ is obtained by deleting the first $k$ members of $\{a_{n}\}$, then $\{b_{n}\}$ is convergent iff $\{a_{n}\}$ is convergent.

Published on 07 Sep 2018 - 0:13

score 88 · Answer 12 · 2026-03-28 03:55:28

88

Views

For what values of $x$ in $(-3,17)$ does the series $\sum\limits^{\infty}_{n=1}\frac{(-1)^n x^n}{n[\log (n+1)]^2}$ converge?

Published on 28 Mar 2026 - 3:55

score 76 · Answer 13 · 2018-09-08 09:28:52

76

Views

Radius of Convergence for the Power Series Solution of $\ u''+(x+1)u'-u=0$

Published on 08 Sep 2018 - 9:28

score 1.6k · Answer 14 · 2026-03-25 03:02:09

1.6k

Views

Show that the series converges and find its sum

Published on 25 Mar 2026 - 3:02

score 68 · Answer 15 · 2026-03-30 08:19:12

68

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Closed set in a finite-dimensional normed space.

Published on 30 Mar 2026 - 8:19

List Question

If $A \subset \mathbb{R}^n$ is bounded an open then every sequence of $A$ has a subsequence that converges to a point of $A$

Every convergent sequence $(x_n)$ is bounded in $(M,d)$

If $f(x)=\sum^{\infty}_{n=0}a_n x^n$ converges for $x=50$, can $f$ be uniformly continuous over $[0,10]$?

If ${a_n}$ converges, then ${a_{2n}}$ converges proof question

Let $\{a_n\}$ be a decreasing sequence of positive real numbers converging to $0,$ then $\sum^{\infty}_{n=1}(-1)^{n}a_n$ converges

Lagrange’s Remainder Theorem

Convergence of $\sum_{n=1}^{\infty}(-n)^{\lfloor\alpha\rfloor}\frac{\sin^3\left(\frac{1}{n}\right)}{\left(\log(n)\right)^{\alpha-1}}$

finding limit of a sequence of vectors

Easy Lim Sup Proof?

Convergence of expectations of product of r.v.

If $\{b_{n}\}$ is obtained by deleting the first $k$ members of $\{a_{n}\}$, then $\{b_{n}\}$ is convergent iff $\{a_{n}\}$ is convergent.

For what values of $x$ in $(-3,17)$ does the series $\sum\limits^{\infty}_{n=1}\frac{(-1)^n x^n}{n[\log (n+1)]^2}$ converge?

Radius of Convergence for the Power Series Solution of $\ u''+(x+1)u'-u=0$

Show that the series converges and find its sum

Closed set in a finite-dimensional normed space.

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