Question

Show that $\{ x = (x_n) \in H^\infty: |x_k| < 1, k = 1, …, N\}$ is open in $H^\infty$

score 105 · Answer 1 · 2026-04-17 10:01:17

105

Views

Show that $\{ x = (x_n) \in H^\infty: |x_k| < 1, k = 1, …, N\}$ is open in $H^\infty$

Published on 17 Apr 2026 - 10:01

score 78 · Answer 2 · 2026-04-15 19:04:01

78

Views

Find x so that $\sum^{\infty}_{n=1}{\frac{1}{(x-1)^n\sqrt{n+5}}}$ converges

Published on 15 Apr 2026 - 19:04

score 38 · Answer 3 · 2026-04-12 13:06:37

38

Views

Divisibility of a sequence of numbers

Published on 12 Apr 2026 - 13:06

score 176 · Answer 4 · 2026-04-17 09:16:47

176

Views

How to evaluate $1+\frac{2^2}{3!}+\frac{3^2}{5!}+\frac{4^2}{7!}+\cdots$?

Published on 17 Apr 2026 - 9:16

score 43 · Answer 5 · 2026-04-10 02:19:41

43

Views

Is $F\subset l_\infty$ closed?

Published on 10 Apr 2026 - 2:19

score 286 · Answer 6 · 2026-04-12 13:05:37

286

Views

How to prove two sequence have a common limit.

Published on 12 Apr 2026 - 13:05

score 1.3k · Answer 7 · 2026-04-17 07:52:11

1.3k

Views

Sequence of positive terms with $\lim a_n=0$ and $ c>0$ such that $|a_{n+1}-a_n|\leq c\cdot a_n^2$.

Published on 17 Apr 2026 - 7:52

score 322 · Answer 8 · 2026-05-16 10:14:38

322

Views

Limit of a recurrence relation when n approaches infinity

Published on 16 May 2026 - 10:14

score 261 · Answer 9 · 2026-04-14 20:12:04

261

Views

Cauchy sequence where the set of outputs is finite

Published on 14 Apr 2026 - 20:12

score 161 · Answer 10 · 2026-04-17 03:01:30

$ \frac{\pi^2\csc^2(\pi/x)}{x^2}= \sum_{n=-\infty}^\infty\frac{1+(xn)^2}{(1-(xn)^2)^2}$. Where can I find some more series of this class?

score 98 · Answer 11 · 2026-04-16 06:10:55

98

Views

The value of $\sum_{n=0}^{\infty}\frac{(n+1)^k}{(2n+1)!}$, where $k\in\mathbb{W}$

Published on 16 Apr 2026 - 6:10

score 86 · Answer 12 · 2026-05-10 21:28:32

86

Views

Partial sums of $\frac{\pi}{2}=\sum_{n=0}^\infty \frac{(2n-1)!!}{2^n\cdot n!\cdot (2n+1) }$.

Published on 10 May 2026 - 21:28

score 44 · Answer 13 · 2026-04-14 00:23:13

44

Views

Infinite Sample Space count ability

Published on 14 Apr 2026 - 0:23

score 179 · Answer 14 · 2026-04-15 20:06:30

179

Views

If $a_n\to a$ and $b_n\to b$ then $\frac1n(a_1b_n+a_2b_{n-1}+\cdots+a_nb_1)\to ab$

Published on 15 Apr 2026 - 20:06

score 232 · Answer 15 · 2026-04-14 07:14:46

232

Views

Convergence of $\frac{1}{2n}\sqrt[n]{1^n+2^n+...+(2n)^n}$?

Published on 14 Apr 2026 - 7:14

List Question

Show that $\{ x = (x_n) \in H^\infty: |x_k| < 1, k = 1, …, N\}$ is open in $H^\infty$

Find x so that $\sum^{\infty}_{n=1}{\frac{1}{(x-1)^n\sqrt{n+5}}}$ converges

Divisibility of a sequence of numbers

How to evaluate $1+\frac{2^2}{3!}+\frac{3^2}{5!}+\frac{4^2}{7!}+\cdots$?

Is $F\subset l_\infty$ closed?

How to prove two sequence have a common limit.

Sequence of positive terms with $\lim a_n=0$ and $ c>0$ such that $|a_{n+1}-a_n|\leq c\cdot a_n^2$.

Limit of a recurrence relation when n approaches infinity

Cauchy sequence where the set of outputs is finite

$ \frac{\pi^2\csc^2(\pi/x)}{x^2}= \sum_{n=-\infty}^\infty\frac{1+(xn)^2}{(1-(xn)^2)^2}$. Where can I find some more series of this class?

The value of $\sum_{n=0}^{\infty}\frac{(n+1)^k}{(2n+1)!}$, where $k\in\mathbb{W}$

Partial sums of $\frac{\pi}{2}=\sum_{n=0}^\infty \frac{(2n-1)!!}{2^n\cdot n!\cdot (2n+1) }$.

Infinite Sample Space count ability

If $a_n\to a$ and $b_n\to b$ then $\frac1n(a_1b_n+a_2b_{n-1}+\cdots+a_nb_1)\to ab$

Convergence of $\frac{1}{2n}\sqrt[n]{1^n+2^n+...+(2n)^n}$?

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