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Question about series rearrangement in Baby Rudin (theorem 3.54).

score 761 · Answer 1 · 2026-04-13 17:34:03

761

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Question about series rearrangement in Baby Rudin (theorem 3.54).

Published on 13 Apr 2026 - 17:34

score 640 · Answer 2 · 2026-04-18 13:00:22

640

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How do I derive the Ramanujan Summation of $\sum_{n=1}^{\infty}n^2 = 0$?

Published on 18 Apr 2026 - 13:00

score 361 · Answer 3 · 2026-04-16 11:06:13

361

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Finding $\sum_{i=1}^{100} a_i$ given that $\sqrt{a_1}+\sqrt{a_2-1}+\sqrt{a_3-2}+\dots+\sqrt{a_n-(n-1)}=\frac12(a_1+a_2+\dots+a_n)=\frac{n(n-3)}4$

Published on 16 Apr 2026 - 11:06

score 33 · Answer 4 · 2026-05-10 22:02:49

33

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$\sum_{k=1}^n\sin kx=\frac{\cos\left(\frac{1}2x\right)-\cos\left(n+\frac{1}2\right)x}{2\sin(x/2)},x\neq0,\pm\pi,\pm 2\pi,\ldots$

Published on 10 May 2026 - 22:02

score 140 · Answer 5 · 2026-04-16 01:10:38

140

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Proof on positive sequence with $\limsup_{n} a_n^{1/n}=1$ and $\liminf_{n}a_n^{1/n} <1$

Published on 16 Apr 2026 - 1:10

score 219 · Answer 6 · 2026-04-17 05:20:58

219

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$\prod_{n=0}^\infty(1+x_m)=\sum_{S\in\mathcal{P}_f(\mathbb{W})} \prod_{m\in S}{x_m}$

Published on 17 Apr 2026 - 5:20

score 82 · Answer 7 · 2026-04-15 21:15:55

82

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Chernoff bound $ \mathbb{P} \left\lbrace \Big| X - \mathbb{E}(X) \Big| > t \right\rbrace $

Published on 15 Apr 2026 - 21:15

score 89 · Answer 8 · 2026-04-15 16:52:53

89

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Limit of $\frac{1}{\ln n}\sum_{j=1}^n\frac{x_j}{j}$ in two different cases.

Published on 15 Apr 2026 - 16:52

score 128 · Answer 9 · 2026-04-16 09:28:08

128

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Limits for sequences: Prove that $\lim_{n \rightarrow \infty} \frac{2n^2 - 3n + 5}{9 - n^2} = -2$

Published on 16 Apr 2026 - 9:28

score 66 · Answer 10 · 2026-05-10 18:27:45

66

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Is there a rule behind why $\left \{ 1+(-1/2)^n) \right \}^{+\infty}_{n=1}$ is $a_{n+2}=1/2(a_{n+1}+a_{n}) , a_{0} = 2 , a_{1}=1/2$ in recursive form?

Published on 10 May 2026 - 18:27

score 104 · Answer 11 · 2026-04-14 23:21:31

104

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Interchanging the order of infinite and finite sum

Published on 14 Apr 2026 - 23:21

score 2.2k · Answer 12 · 2026-04-12 15:44:46

2.2k

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How to find the partial sum of $n/2^n$?

Published on 12 Apr 2026 - 15:44

score 347 · Answer 13 · 2026-04-16 22:42:25

347

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Does $b_n = a_{n+1} - a_n $ is a zero sequence implies $a_n$ is convergent?

Published on 16 Apr 2026 - 22:42

score 33 · Answer 14 · 2026-05-10 15:03:29

33

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Growth of "spectral bounded" sequences of products of matrices

Published on 10 May 2026 - 15:03

score 259 · Answer 15 · 2026-04-15 14:58:52

259

Views

Check convergence of the series $\sum_{n=1}^\infty\cos^{n^3}\frac1{\sqrt n}$

Published on 15 Apr 2026 - 14:58

List Question

Question about series rearrangement in Baby Rudin (theorem 3.54).

How do I derive the Ramanujan Summation of $\sum_{n=1}^{\infty}n^2 = 0$?

Finding $\sum_{i=1}^{100} a_i$ given that $\sqrt{a_1}+\sqrt{a_2-1}+\sqrt{a_3-2}+\dots+\sqrt{a_n-(n-1)}=\frac12(a_1+a_2+\dots+a_n)=\frac{n(n-3)}4$

$\sum_{k=1}^n\sin kx=\frac{\cos\left(\frac{1}2x\right)-\cos\left(n+\frac{1}2\right)x}{2\sin(x/2)},x\neq0,\pm\pi,\pm 2\pi,\ldots$

Proof on positive sequence with $\limsup_{n} a_n^{1/n}=1$ and $\liminf_{n}a_n^{1/n} <1$

$\prod_{n=0}^\infty(1+x_m)=\sum_{S\in\mathcal{P}_f(\mathbb{W})} \prod_{m\in S}{x_m}$

Chernoff bound $ \mathbb{P} \left\lbrace \Big| X - \mathbb{E}(X) \Big| > t \right\rbrace $

Limit of $\frac{1}{\ln n}\sum_{j=1}^n\frac{x_j}{j}$ in two different cases.

Limits for sequences: Prove that $\lim_{n \rightarrow \infty} \frac{2n^2 - 3n + 5}{9 - n^2} = -2$

Is there a rule behind why $\left \{ 1+(-1/2)^n) \right \}^{+\infty}_{n=1}$ is $a_{n+2}=1/2(a_{n+1}+a_{n}) , a_{0} = 2 , a_{1}=1/2$ in recursive form?

Interchanging the order of infinite and finite sum

How to find the partial sum of $n/2^n$?

Does $b_n = a_{n+1} - a_n $ is a zero sequence implies $a_n$ is convergent?

Growth of "spectral bounded" sequences of products of matrices

Check convergence of the series $\sum_{n=1}^\infty\cos^{n^3}\frac1{\sqrt n}$

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