Question

Regularized sum of $1+(1+\frac1{2^2}) + (1+\frac1{2^2}+\frac1{3^2})+\cdots$, or $\sum_{k=1}^\infty \sum_{j=1}^k\frac1{j^2}$?

score 426 · Answer 1 · 2026-03-26 23:10:48

426

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Regularized sum of $1+(1+\frac1{2^2}) + (1+\frac1{2^2}+\frac1{3^2})+\cdots$, or $\sum_{k=1}^\infty \sum_{j=1}^k\frac1{j^2}$?

Published on 26 Mar 2026 - 23:10

score 104 · Answer 2 · 2020-12-23 20:53:32

104

Views

The divergence rate of a divergent series

Published on 23 Dec 2020 - 20:53

score 258 · Answer 3 · 2020-12-24 18:52:50

258

Views

Why doesn't Ramanujan summation converge for the geometric series?

Published on 24 Dec 2020 - 18:52

score 286 · Answer 4 · 2026-03-26 13:00:57

286

Views

Corrections to the $\delta$ limit of the Cauchy distribution

Published on 26 Mar 2026 - 13:00

score 334 · Answer 5 · 2020-12-25 18:17:54

334

Views

What is the interval of convergence of the Taylor series $f(x) = \ln(1-x^2)$?

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score 65 · Answer 6 · 2020-12-26 14:50:11

65

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Can convergent series have a non-exist or infinity entry?

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score 160 · Answer 7 · 2020-12-26 21:42:54

160

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Is Cesaro summation always resistant to attack by finitely growing 0s

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score 100 · Answer 8 · 2026-03-27 14:28:45

100

Views

Assigning other finite values to $1 + 2 + 3 + ...$

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score 139 · Answer 9 · 2026-04-03 21:13:28

139

Views

Integration and periodic divergent series

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score 57 · Answer 10 · 2026-03-26 11:18:10

57

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Summation of an infinite series from two ways leading up to two answers

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score 1k · Answer 11 · 2026-04-03 04:01:33

1k

Views

Associated Legendre Polynomials from the Schrodinger Equation for the Hydrogen Atom

Published on 03 Apr 2026 - 4:01

score 107 · Answer 12 · 2021-01-18 13:02:47

107

Views

$\lim_{|z| \to 1 } |f(z)| = \infty$ for $f(z) = \sum_{k=1}^\infty z^{k!}$, a strange series manipulation

Published on 18 Jan 2021 - 13:02

score 1.3k · Answer 13 · 2026-03-28 13:38:40

1.3k

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Why is the integral test only for positive decreasing functions?

Published on 28 Mar 2026 - 13:38

score 88 · Answer 14 · 2026-03-26 23:11:34

88

Views

Evaluate $\zeta_F(0)$ where $F = \mathbb{Q}(\sqrt{-23})$

Published on 26 Mar 2026 - 23:11

score 89 · Answer 15 · 2021-01-29 21:50:55

89

Views

If $a_k>0\ \forall\ k\in \mathbb{N}\ $ and $r>0,\ $ prove that $\sum\frac{1}{a_k}$ converges $\iff \sum\frac{1}{a_k+r}$ converges.

Published on 29 Jan 2021 - 21:50

List Question

Regularized sum of $1+(1+\frac1{2^2}) + (1+\frac1{2^2}+\frac1{3^2})+\cdots$, or $\sum_{k=1}^\infty \sum_{j=1}^k\frac1{j^2}$?

The divergence rate of a divergent series

Why doesn't Ramanujan summation converge for the geometric series?

Corrections to the $\delta$ limit of the Cauchy distribution

What is the interval of convergence of the Taylor series $f(x) = \ln(1-x^2)$?

Can convergent series have a non-exist or infinity entry?

Is Cesaro summation always resistant to attack by finitely growing 0s

Assigning other finite values to $1 + 2 + 3 + ...$

Integration and periodic divergent series

Summation of an infinite series from two ways leading up to two answers

Associated Legendre Polynomials from the Schrodinger Equation for the Hydrogen Atom

$\lim_{|z| \to 1 } |f(z)| = \infty$ for $f(z) = \sum_{k=1}^\infty z^{k!}$, a strange series manipulation

Why is the integral test only for positive decreasing functions?

Evaluate $\zeta_F(0)$ where $F = \mathbb{Q}(\sqrt{-23})$

If $a_k>0\ \forall\ k\in \mathbb{N}\ $ and $r>0,\ $ prove that $\sum\frac{1}{a_k}$ converges $\iff \sum\frac{1}{a_k+r}$ converges.

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