Question

Sum of the given cosine series

score 145 · Answer 1 · 2026-04-14 19:36:26

145

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Sum of the given cosine series

Published on 14 Apr 2026 - 19:36

score 108 · Answer 2 · 2026-04-17 07:49:23

108

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Existence of natural number in the set $\left\{x \textrm{ } | \textrm{ } Q \leq \sin(x) < 1\right\} $, $0 < Q < 1$

Published on 17 Apr 2026 - 7:49

score 81 · Answer 3 · 2026-04-16 08:27:09

81

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Summing infinite series $\sum_{n=0}^\infty\frac{\cos^{2n+1}x}{2n+1}$.

Published on 16 Apr 2026 - 8:27

score 467 · Answer 4 · 2026-04-14 19:18:50

467

Views

Show using the definition of convergence that the sequence 1/n does not converge to any number $L > 0$.

Published on 14 Apr 2026 - 19:18

score 3.8k · Answer 5 · 2026-04-14 20:43:20

3.8k

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Does the series for $\cos(x)/x$ converges?

Published on 14 Apr 2026 - 20:43

score 38 · Answer 6 · 2026-05-15 04:18:34

38

Views

Show uniform convergence of series with |x|

Published on 15 May 2026 - 4:18

score 410 · Answer 7 · 2026-04-11 14:05:36

410

Views

Theorem stating the connection of limits of sequences and functions.

Published on 11 Apr 2026 - 14:05

score 40 · Answer 8 · 2026-04-13 03:15:54

40

Views

Uniformly convergence of a sequence defined in compact set.

Published on 13 Apr 2026 - 3:15

score 1.8k · Answer 9 · 2026-05-15 20:54:21

1.8k

Views

Generating function for the number of unlabeled trees on $n$ vertices

Published on 15 May 2026 - 20:54

score 103 · Answer 10 · 2026-04-13 19:52:27

103

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Does the series $\sum_{k=1}^{\infty} (\sin \frac{1}{k} - \arctan\frac{1}{k})$ converge?

Published on 13 Apr 2026 - 19:52

score 106 · Answer 11 · 2026-05-10 21:11:55

106

Views

Determine Convergence of $\sum_{n=1}^\infty \frac{(-1)^nn!}{(n+100)!}$

Published on 10 May 2026 - 21:11

score 432 · Answer 12 · 2026-04-16 20:59:58

432

Views

Show convergence and find the limit of the sequence given by $a_1=1$ and $a_{n+1}=\frac{1}{3+a_n}$

Published on 16 Apr 2026 - 20:59

score 100 · Answer 13 · 2026-04-15 14:21:26

100

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$\{u_j\}$ an harmonic sequence, $\{\partial^{\alpha}, |\alpha|\le 2\}$ converges uniformly, $u = \lim_j u_j$ is harmonic in $\Omega$

Published on 15 Apr 2026 - 14:21

score 101 · Answer 14 · 2026-05-15 17:29:00

101

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What is $\lim_{n\to\infty}\int_{0}^\infty \exp(-x^n \arctan(\frac1x)) dx,n>1$

Published on 15 May 2026 - 17:29

score 24.1k · Answer 15 · 2026-04-12 04:39:51

24.1k

Views

What is a binary expansion of a real number?

Published on 12 Apr 2026 - 4:39

List Question

Sum of the given cosine series

Existence of natural number in the set $\left\{x \textrm{ } | \textrm{ } Q \leq \sin(x) < 1\right\} $, $0 < Q < 1$

Summing infinite series $\sum_{n=0}^\infty\frac{\cos^{2n+1}x}{2n+1}$.

Show using the definition of convergence that the sequence 1/n does not converge to any number $L > 0$.

Does the series for $\cos(x)/x$ converges?

Show uniform convergence of series with |x|

Theorem stating the connection of limits of sequences and functions.

Uniformly convergence of a sequence defined in compact set.

Generating function for the number of unlabeled trees on $n$ vertices

Does the series $\sum_{k=1}^{\infty} (\sin \frac{1}{k} - \arctan\frac{1}{k})$ converge?

Determine Convergence of $\sum_{n=1}^\infty \frac{(-1)^nn!}{(n+100)!}$

Show convergence and find the limit of the sequence given by $a_1=1$ and $a_{n+1}=\frac{1}{3+a_n}$

$\{u_j\}$ an harmonic sequence, $\{\partial^{\alpha}, |\alpha|\le 2\}$ converges uniformly, $u = \lim_j u_j$ is harmonic in $\Omega$

What is $\lim_{n\to\infty}\int_{0}^\infty \exp(-x^n \arctan(\frac1x)) dx,n>1$

What is a binary expansion of a real number?

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