List questions from harmonic-numbers

Published on 01 Jun 2016 - 23:08

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Tail bound for the truncated random harmonic series

Published on 11 Jun 2016 - 22:07

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Are we guaranteed that the harmonic series minus infinite random terms always converge?

Published on 14 Jun 2016 - 13:16

211

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Generalizing a Telescoping Sum $\sum_{n=1}^\infty \frac{1}{n+k}-\frac{1}{n}$

Published on 18 Jun 2016 - 17:20

2.3k

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Evaluating $\int_0^1 \frac{\arctan x \log x}{1+x}dx$

Published on 28 Jun 2016 - 9:56

2.6k

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Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$

Published on 24 Feb 2026 - 6:51

128

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Genereating function of $H_{2n}$

Published on 02 Jul 2016 - 4:39

556

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Is the following Harmonic Number Identity true?

Published on 27 Mar 2026 - 22:11

206

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Fibonacci summation

Published on 27 Mar 2026 - 5:09

1.9k

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Reference for proof of harmonic number asymptotic expansion

Published on 26 Mar 2026 - 12:06

1.2k

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How to calculate $\sum_{n=1}^\infty\frac{(-1)^n}n H_n^2$?

Published on 29 May 2013 - 4:11

1.4k

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A challenging logarithmic integral $\int_0^1 \frac{\log(1+x)\log(1-x)}{1+x}dx$

Published on 01 Jun 2013 - 7:28

1.2k

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Harmonic number divided by n

Published on 02 Jun 2013 - 14:41

377

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Need to show that $\lim_{x\to\infty}\left(\sum_{n\le x}^{}\frac{1}{n}-\ln x \right)$ exist and is less than $1$

Published on 26 Mar 2026 - 12:08

702

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Integral of polylogarithms and logs in closed form: $\int_0^1 \frac{du}{u}\text{Li}_2(u)^2(\log u)^2$

Published on 19 Jun 2013 - 19:45

List Question

An interesting inequality $\sum_{k=1}^n \frac{1}{n+k}<\frac{\sqrt{2}}{2}, \ n\ge1$

Tail bound for the truncated random harmonic series

Are we guaranteed that the harmonic series minus infinite random terms always converge?

Generalizing a Telescoping Sum $\sum_{n=1}^\infty \frac{1}{n+k}-\frac{1}{n}$

Evaluating $\int_0^1 \frac{\arctan x \log x}{1+x}dx$

Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$

Genereating function of $H_{2n}$

Is the following Harmonic Number Identity true?

Fibonacci summation

Reference for proof of harmonic number asymptotic expansion

How to calculate $\sum_{n=1}^\infty\frac{(-1)^n}n H_n^2$?

A challenging logarithmic integral $\int_0^1 \frac{\log(1+x)\log(1-x)}{1+x}dx$

Harmonic number divided by n

Need to show that $\lim_{x\to\infty}\left(\sum_{n\le x}^{}\frac{1}{n}-\ln x \right)$ exist and is less than $1$

Integral of polylogarithms and logs in closed form: $\int_0^1 \frac{du}{u}\text{Li}_2(u)^2(\log u)^2$

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