List questions from convergence-divergence

Published on 09 Jun 2018 - 7:17

288

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Is the integral test necessary and sufficient for convergence?

Published on 29 Mar 2026 - 12:43

43

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What is an "optimal convergence rate" ?

Published on 09 Jun 2018 - 11:40

101

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$f(z)=\sum_{k=1}^{\infty}\frac{1}{(z-k)^2}+\sum_{k=1}^{\infty}\frac{1}{(z+k)^2}+\frac{1}{z^2}$ holomorphic. $z \in \mathbb{C} \setminus \mathbb{Z}$

Published on 09 Jun 2018 - 12:15

161

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Convergence of the integral of non negative functions

Published on 26 Mar 2026 - 2:56

49

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Suppose $f(x)$ monotonous decreases on $[0,+\infty) $

Published on 10 Jun 2018 - 8:33

1.2k

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sample variance converges almost surely

Published on 26 Mar 2026 - 14:32

218

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If a series converges, does the sequence of its summands necessarily converge to zero?

Published on 10 Jun 2018 - 12:56

56

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If $f_n \to f$ in $\|\cdot\|$, then $\|f_n\| \to \|f\|$. When is the converse true?

Published on 25 Mar 2026 - 21:51

161

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The sequence $(\frac{1}{n})$ using the discrete metric is Cauchy?

Published on 25 Mar 2026 - 12:19

165

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Studying a limit for proving the convergence of Bertrand series.

Published on 10 Jun 2018 - 23:23

47

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How do we know/prove a complex power series converges? and how do we get the domain of convergence?

Published on 11 Jun 2018 - 2:00

249

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Generalized Egoroff's Theorem

Published on 24 Mar 2026 - 22:06

475

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Gradient descent converges to critical points for non-convex functions

Published on 25 Mar 2026 - 11:01

38

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Radius of convergence of a power series convergent for $s \in [0,1)$

Published on 27 Mar 2026 - 11:48

List Question

Does the function $H_{\lfloor x \rfloor} - \log(x)$ converge?

Is the integral test necessary and sufficient for convergence?

What is an "optimal convergence rate" ?

$f(z)=\sum_{k=1}^{\infty}\frac{1}{(z-k)^2}+\sum_{k=1}^{\infty}\frac{1}{(z+k)^2}+\frac{1}{z^2}$ holomorphic. $z \in \mathbb{C} \setminus \mathbb{Z}$

Convergence of the integral of non negative functions

Suppose $f(x)$ monotonous decreases on $[0,+\infty) $

sample variance converges almost surely

If a series converges, does the sequence of its summands necessarily converge to zero?

If $f_n \to f$ in $\|\cdot\|$, then $\|f_n\| \to \|f\|$. When is the converse true?

The sequence $(\frac{1}{n})$ using the discrete metric is Cauchy?

Studying a limit for proving the convergence of Bertrand series.

How do we know/prove a complex power series converges? and how do we get the domain of convergence?

Generalized Egoroff's Theorem

Gradient descent converges to critical points for non-convex functions

Radius of convergence of a power series convergent for $s \in [0,1)$

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