List questions from divergent-series

Published on 19 Apr 2016 - 12:15

4k

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Show that $f(z)=\sum_{n=0}^{\infty}z^{2^n}$ can't be analytically continued past the unit disk.

Published on 27 Mar 2026 - 1:46

99

Views

A way to evaluate $\sum_{n=0}^\infty(-1)^{n+1}n$

Published on 19 Apr 2016 - 23:56

87

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Examine convergence and (almost) uniform convergence of $\sum_{n=1}^{+ \infty} \frac{n^2 x^2}{e^{n^2 |x|}}$ for $x \in \mathbb{R}$.

Published on 20 Apr 2016 - 12:03

959

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How does zeta of zero equal to negative one half rather than to infinity?

Published on 26 Mar 2026 - 4:16

72

Views

Converging or Diverging Series

Published on 22 Apr 2016 - 17:18

1.3k

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Convergence of $\sum _{n=3} ^\infty \frac 1 {(\ln \ln n)^{\ln \ln n}}$

Published on 22 Apr 2016 - 17:48

135

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Good problems to do while reading Hardy's book on divergent series?

Published on 25 Apr 2016 - 12:59

101

Views

Why does this Calculus II sequence diverge?

Published on 25 Apr 2016 - 15:13

78

Views

Prove the divergent series $\sum_{k=2}^{\infty} \frac{1}{log^3k}$

Published on 25 Apr 2016 - 21:53

208

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Does the series converge

Published on 29 Apr 2016 - 18:43

71

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Tricky divergent binomial expansions?

Published on 02 May 2016 - 22:05

163

Views

Can we cover the entire plane with the square with area 1/n for each positive integer n?

Published on 27 Mar 2026 - 18:09

232

Views

Smallest $x$ for which $\sum_{n=1}^{\infty}\dfrac{1}{n^x}$ converges

Published on 04 May 2016 - 13:44

777

Views

Can we show that $1+2+3+\dotsb=-\frac{1}{12}$ using only stability or linearity, not both, and without regularizing or specifying a summation method?

Published on 23 Feb 2026 - 14:08

List Question

About the comparison test

Show that $f(z)=\sum_{n=0}^{\infty}z^{2^n}$ can't be analytically continued past the unit disk.

A way to evaluate $\sum_{n=0}^\infty(-1)^{n+1}n$

Examine convergence and (almost) uniform convergence of $\sum_{n=1}^{+ \infty} \frac{n^2 x^2}{e^{n^2 |x|}}$ for $x \in \mathbb{R}$.

How does zeta of zero equal to negative one half rather than to infinity?

Converging or Diverging Series

Convergence of $\sum _{n=3} ^\infty \frac 1 {(\ln \ln n)^{\ln \ln n}}$

Good problems to do while reading Hardy's book on divergent series?

Why does this Calculus II sequence diverge?

Prove the divergent series $\sum_{k=2}^{\infty} \frac{1}{log^3k}$

Does the series converge

Tricky divergent binomial expansions?

Can we cover the entire plane with the square with area 1/n for each positive integer n?

Smallest $x$ for which $\sum_{n=1}^{\infty}\dfrac{1}{n^x}$ converges

Can we show that $1+2+3+\dotsb=-\frac{1}{12}$ using only stability or linearity, not both, and without regularizing or specifying a summation method?

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