List questions from harmonic-numbers

Published on 05 Mar 2018 - 5:51

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How to show $\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}=2$?

Published on 11 Mar 2018 - 2:09

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Problem involving harmonic number

Published on 22 Mar 2026 - 0:27

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If $a$, $b$, $c$ are three positive numbers in harmonic sequence, show that $a^2+c^2>2b^2$.

Published on 24 Mar 2026 - 12:39

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How do we rearrange the terms of the harmonic series so they add up to 0

Published on 22 Mar 2026 - 19:29

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Relation between harmonic series $H(m)$ and polygamma function?

Published on 15 Mar 2026 - 6:05

207

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Analytic properties of Euler sums

Published on 24 Mar 2026 - 22:08

180

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General formula for $\frac{1}{1} + \frac{1}{2}+\frac{1}{3} ... +\frac{1}{n} $

Published on 20 Apr 2018 - 4:28

89

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Sum series product

Published on 21 Mar 2026 - 14:44

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Why is $\left(\frac{1}{y} + \frac{1}{z}\right)\left(\frac{1}{z} + \frac{1}{x}\right)\left(\frac{1}{x} + \frac{1}{y}\right) \geq \frac{8}{xyz}$?

Published on 17 Mar 2026 - 22:30

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Is there a reason why this function does not exist/can't be found?

Published on 23 Mar 2026 - 11:13

80

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Approximation to a partial sum

Published on 22 Mar 2026 - 4:31

199

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Prove that $\lim\limits_{n\to\infty}\frac{1}{n}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\right)=0$

Published on 18 May 2018 - 6:43

146

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Mellin Transform

Published on 20 Mar 2026 - 7:21

116

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Prove that $1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2^n-1}<n$ for $n\geq{2}$

Published on 07 Jun 2018 - 11:19

List Question

Elementary proof of $\sum_{k=1}^{n}\frac{1}{2k+1}$ with all odd denominators is never an integer?

How to show $\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}=2$?

Problem involving harmonic number

If $a$, $b$, $c$ are three positive numbers in harmonic sequence, show that $a^2+c^2>2b^2$.

How do we rearrange the terms of the harmonic series so they add up to 0

Relation between harmonic series $H(m)$ and polygamma function?

Analytic properties of Euler sums

General formula for $\frac{1}{1} + \frac{1}{2}+\frac{1}{3} ... +\frac{1}{n} $

Sum series product

Why is $\left(\frac{1}{y} + \frac{1}{z}\right)\left(\frac{1}{z} + \frac{1}{x}\right)\left(\frac{1}{x} + \frac{1}{y}\right) \geq \frac{8}{xyz}$?

Is there a reason why this function does not exist/can't be found?

Approximation to a partial sum

Prove that $\lim\limits_{n\to\infty}\frac{1}{n}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\right)=0$

Mellin Transform

Prove that $1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2^n-1}<n$ for $n\geq{2}$

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