Question

Closed form for the integral $\int_0^1 \frac{dy}{1+y^2} \tanh^{-1} \frac{1}{\sqrt{3+y^2}}$

score 259 · Answer 1 · 2026-04-16 12:22:13

259

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Closed form for the integral $\int_0^1 \frac{dy}{1+y^2} \tanh^{-1} \frac{1}{\sqrt{3+y^2}}$

Published on 16 Apr 2026 - 12:22

score 124 · Answer 2 · 2026-04-15 18:03:07

124

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Prove explicit form of a recursive sequence

Published on 15 Apr 2026 - 18:03

score 90 · Answer 3 · 2026-04-10 21:22:13

90

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what is the relationship between $X$ and Discrete Fourier Transform of $\overline{x}$

Published on 10 Apr 2026 - 21:22

score 45 · Answer 4 · 2026-04-16 18:47:26

45

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Proofcheck: Let $(a_{n})_{n\in\mathbb{N}}$ be an increasing and bounded sequence. Prove that $a_{n}\rightarrow\sup{(a_{n})}$.

Published on 16 Apr 2026 - 18:47

score 621 · Answer 5 · 2026-04-14 19:53:23

621

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Limit of a Piecewise Sequence

Published on 14 Apr 2026 - 19:53

score 45 · Answer 6 · 2026-04-15 18:11:05

45

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Prove that $\{ x_n \}^\infty_{i=0}$ where $x_n = r^n$ is a Cauchy sequence (where $0<r<1$)

Published on 15 Apr 2026 - 18:11

score 57 · Answer 7 · 2026-04-15 08:21:01

If the series $ \ \sum_{n=1}^{\infty} a_n^2 \ $ converges , then the $ \ n^{th } \ $ term $ \ a_n^2 \ \to 0 \ \ as \ \ n \to \infty $

score 93 · Answer 8 · 2026-04-16 17:31:45

93

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$ \sum_{n=1}^{\infty} a_n \ $ converges then show that $ \ |a_n|<1 \ $

Published on 16 Apr 2026 - 17:31

score 582 · Answer 9 · 2026-04-13 02:44:46

582

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Series expansion involving fractional powers

Published on 13 Apr 2026 - 2:44

score 59 · Answer 10 · 2026-04-16 08:00:27

59

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Limit of the series $\lim_{n\rightarrow \infty}\frac{1}{s_n}\sum_{k=1}^{n}a_kx_k$

Published on 16 Apr 2026 - 8:00

score 867 · Answer 11 · 2026-04-13 16:15:38

867

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Limit of a sequence related to Cesaro sum

Published on 13 Apr 2026 - 16:15

score 41 · Answer 12 · 2026-04-20 21:00:15

41

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Clustering via Pattern Formation

Published on 20 Apr 2026 - 21:00

score 69 · Answer 13 · 2026-04-15 13:11:37

69

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How To find the 1991-th number of this series

Published on 15 Apr 2026 - 13:11

score 45 · Answer 14 · 2026-04-16 04:28:55

45

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Product space is completed with metric $d(x,y):=\sum_{i\in\mathbb{N}}\min\{2^{-i},d_i(x_i,y_i)\}.$

Published on 16 Apr 2026 - 4:28

score 86 · Answer 15 · 2026-04-13 08:21:46

86

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Closed form the following series

Published on 13 Apr 2026 - 8:21

List Question

Closed form for the integral $\int_0^1 \frac{dy}{1+y^2} \tanh^{-1} \frac{1}{\sqrt{3+y^2}}$

Prove explicit form of a recursive sequence

what is the relationship between $X$ and Discrete Fourier Transform of $\overline{x}$

Proofcheck: Let $(a_{n})_{n\in\mathbb{N}}$ be an increasing and bounded sequence. Prove that $a_{n}\rightarrow\sup{(a_{n})}$.

Limit of a Piecewise Sequence

Prove that $\{ x_n \}^\infty_{i=0}$ where $x_n = r^n$ is a Cauchy sequence (where $0<r<1$)

If the series $ \ \sum_{n=1}^{\infty} a_n^2 \ $ converges , then the $ \ n^{th } \ $ term $ \ a_n^2 \ \to 0 \ \ as \ \ n \to \infty $

$ \sum_{n=1}^{\infty} a_n \ $ converges then show that $ \ |a_n|<1 \ $

Series expansion involving fractional powers

Limit of the series $\lim_{n\rightarrow \infty}\frac{1}{s_n}\sum_{k=1}^{n}a_kx_k$

Limit of a sequence related to Cesaro sum

Clustering via Pattern Formation

How To find the 1991-th number of this series

Product space is completed with metric $d(x,y):=\sum_{i\in\mathbb{N}}\min\{2^{-i},d_i(x_i,y_i)\}.$

Closed form the following series

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