Question

Why do we ask for absolute convergence of a series to define the mean of a discrete random variable?

score 2.2k · Answer 1 · 2026-03-26 00:53:38

2.2k

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Why do we ask for absolute convergence of a series to define the mean of a discrete random variable?

Published on 26 Mar 2026 - 0:53

score 225 · Answer 2 · 2021-05-03 05:13:14

225

Views

$f\ge0$ is monotone such that $\int_0^\infty f(x)\sin xdx$ converges absolutely then the improper integral of $f$ converges

Published on 03 May 2021 - 5:13

score 74 · Answer 3 · 2021-05-05 13:22:15

74

Views

Prove that $\int_a^\infty f\ dx$ exists if $f\geq0$, monotone, continuously differentiable, and $\int_a^\infty f(x)\sin(x)\ dx$ absolutely converges

Published on 05 May 2021 - 13:22

score 170 · Answer 4 · 2021-05-19 04:25:47

170

Views

Prove that the series converges absolutely for all $z \in \mathbb C$ with $|z|=1$

Published on 19 May 2021 - 4:25

score 88 · Answer 5 · 2021-05-22 14:58:16

88

Views

Does $\sum_{n=1}^\infty(1- \sqrt[n]{n})^n$ converge absolutely?

Published on 22 May 2021 - 14:58

score 181 · Answer 6 · 2021-05-23 12:34:49

181

Views

Does $\sum_{n=1}^\infty\sin(n)/\sqrt n$ converge absolutely?

Published on 23 May 2021 - 12:34

score 234 · Answer 7 · 2021-06-16 14:38:25

234

Views

Convergence of the product of a convergent and absolutely convergent series' elements.

Published on 16 Jun 2021 - 14:38

score 633 · Answer 8 · 2021-06-29 02:22:58

633

Views

Interchanging integral and sum in case of absolute and uniform convergence

Published on 29 Jun 2021 - 2:22

score 642 · Answer 9 · 2026-03-26 00:53:41

642

Views

Can a power series conditionally converge outside its radius of convergence?

Published on 26 Mar 2026 - 0:53

score 149 · Answer 10 · 2021-07-04 11:27:02

149

Views

A theorem about absolutely convergent series. Please tell me a rigorous proof.

Published on 04 Jul 2021 - 11:27

score 207 · Answer 11 · 2021-07-06 16:30:21

207

Views

Absolute convergence implies convergence.

Published on 06 Jul 2021 - 16:30

score 269 · Answer 12 · 2021-07-06 18:18:16

269

Views

Absolute convergence in normed space

Published on 06 Jul 2021 - 18:18

score 79 · Answer 13 · 2021-07-07 03:41:31

79

Views

Convervence in the normed space.

Published on 07 Jul 2021 - 3:41

score 116 · Answer 14 · 2021-07-11 13:01:48

116

Views

If $\sum f_j^2 $ and $\sum g_j^2$ conrverge uniformly, show that $\sum f_j g_j$ converges absolutely and uniformly

Published on 11 Jul 2021 - 13:01

score 1.2k · Answer 15 · 2026-02-26 01:22:25

1.2k

Views

Uniform convergent of $\sum x^n/n$

Published on 26 Feb 2026 - 1:22

List Question

Why do we ask for absolute convergence of a series to define the mean of a discrete random variable?

$f\ge0$ is monotone such that $\int_0^\infty f(x)\sin xdx$ converges absolutely then the improper integral of $f$ converges

Prove that $\int_a^\infty f\ dx$ exists if $f\geq0$, monotone, continuously differentiable, and $\int_a^\infty f(x)\sin(x)\ dx$ absolutely converges

Prove that the series converges absolutely for all $z \in \mathbb C$ with $|z|=1$

Does $\sum_{n=1}^\infty(1- \sqrt[n]{n})^n$ converge absolutely?

Does $\sum_{n=1}^\infty\sin(n)/\sqrt n$ converge absolutely?

Convergence of the product of a convergent and absolutely convergent series' elements.

Interchanging integral and sum in case of absolute and uniform convergence

Can a power series conditionally converge outside its radius of convergence?

A theorem about absolutely convergent series. Please tell me a rigorous proof.

Absolute convergence implies convergence.

Absolute convergence in normed space

Convervence in the normed space.

If $\sum f_j^2 $ and $\sum g_j^2$ conrverge uniformly, show that $\sum f_j g_j$ converges absolutely and uniformly

Uniform convergent of $\sum x^n/n$

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