List questions from harmonic-numbers

Published on 06 Jul 2013 - 15:28

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Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$

Published on 08 Jul 2013 - 20:46

20.2k

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How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$?

Published on 25 Jul 2013 - 2:51

2.6k

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Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$

Published on 01 Aug 2013 - 16:31

463

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Interesting Harmonic Sum $\sum_{k\geq 1}\frac{(-1)^{k-1}}{k^2}H_k^{(2)}$

Published on 03 Aug 2013 - 15:41

1.7k

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Definite Dilogarithm integral $\int^1_0 \frac{\operatorname{Li}_2^2(x)}{x}\, dx $

Published on 27 Mar 2026 - 22:12

533

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$\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?

Published on 11 Aug 2013 - 11:58

1.8k

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Evaluating $\int^1_0 \frac{\log(1+x)\log(1-x) \log(x)}{x}\, \mathrm dx$

Published on 12 Aug 2013 - 2:04

877

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Evaluating $\int^1_0 \frac{\operatorname{Li}_3(x)}{1-x} \log(x)\, \mathrm dx$

Published on 27 Mar 2026 - 23:48

10k

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Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

Published on 25 Mar 2026 - 6:04

752

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Dilogarithm integral $\int^x_0 \frac{\operatorname{Li}_2(1-t)\log(1-t)}{t}\, dt$

Published on 27 Mar 2026 - 23:48

206

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Generating function for $\sum_{k\geq 1} H^{(k)}_n x^ k $

Published on 27 Mar 2026 - 23:57

173

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Proving there don't exist $F(x), G(x)$ such that $1^{-1}+2^{-1}+3^{-1}+\cdots+n^{-1}={F(n)}/{G(n)}$

Published on 02 Sep 2013 - 14:25

77.1k

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Is there a partial sum formula for the Harmonic Series?

Published on 17 Sep 2013 - 6:03

738

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Prove limit of $\frac1{n+1}+\frac1{n+2}+\ldots+\frac1{n+n}$ exists and lies between $0$ and $1$.

Published on 19 Sep 2013 - 0:15

List Question

Proving Binomial Identity without calculus

Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$

How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$?

Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$

Interesting Harmonic Sum $\sum_{k\geq 1}\frac{(-1)^{k-1}}{k^2}H_k^{(2)}$

Definite Dilogarithm integral $\int^1_0 \frac{\operatorname{Li}_2^2(x)}{x}\, dx $

$\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?

Evaluating $\int^1_0 \frac{\log(1+x)\log(1-x) \log(x)}{x}\, \mathrm dx$

Evaluating $\int^1_0 \frac{\operatorname{Li}_3(x)}{1-x} \log(x)\, \mathrm dx$

Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

Dilogarithm integral $\int^x_0 \frac{\operatorname{Li}_2(1-t)\log(1-t)}{t}\, dt$

Generating function for $\sum_{k\geq 1} H^{(k)}_n x^ k $

Proving there don't exist $F(x), G(x)$ such that $1^{-1}+2^{-1}+3^{-1}+\cdots+n^{-1}={F(n)}/{G(n)}$

Is there a partial sum formula for the Harmonic Series?

Prove limit of $\frac1{n+1}+\frac1{n+2}+\ldots+\frac1{n+n}$ exists and lies between $0$ and $1$.

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