List questions from harmonic-numbers

Published on 26 Mar 2026 - 4:36

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Harmonic Series divergence - induction proof

Published on 10 Nov 2019 - 12:50

382

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Challenging Integral: $\int_0^\infty\frac{\ln(2+x)\operatorname{Li}_2(-x)}{x(2+x)}dx$

Published on 11 Nov 2019 - 6:27

210

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How to compute $\sum_{n=1}^\infty\frac{(-1)^nH_{n/2}}{n^4}$?

Published on 12 Nov 2019 - 21:15

88

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How to prove $n \ge 2 {\left ( \sum_{k=1}^n \frac{1}{k} \right)}^2$ for all $n \ge 2$?

Published on 13 Nov 2019 - 10:50

201

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Compute $\int_0^1\frac{\tan^{-1}(x)\ln(1+x^2)}{x(1+x)}dx$ using harmonic series

Published on 15 Nov 2019 - 21:13

327

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Evaluating $\int_0^{\pi/2} \frac{t \ln (1-\sin{t})}{\sin t} dt$

Published on 16 Nov 2019 - 19:15

445

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How to find $I=\int_0^1\frac{\arctan^2x}{1+x}\left(\frac{\ln x}{1-x}+\ln(1+x)\right)dx$

Published on 26 Mar 2026 - 8:02

146

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Sum of Scaled Harmonic Numbers

Published on 20 Nov 2019 - 5:22

746

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Challenging Sum: compute $\sum_{n=1}^\infty\frac{H_n}{2n+1}\left(\zeta(3)-H_n^{(3)}\right)$

Published on 26 Mar 2026 - 7:59

85

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Simplify a sum of harmonic numbers

Published on 20 Nov 2019 - 12:12

453

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How to compute $\sum_{n=1}^\infty\frac{(-1)^nH_n}{n^4}$ by real integration only?

Published on 25 Nov 2019 - 4:27

505

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An attempt to prove the generalization of $\sum_{n=1}^\infty \frac{(-1)^nH_n}{n^{2a}}$

Published on 26 Nov 2019 - 3:51

521

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Compute $\int_0^1\frac{\ln^2(1+x)\operatorname{Li}_2(-x)}{x}dx$

Published on 26 Mar 2026 - 7:59

233

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Closed expression for sum $\sum_{k = 1}^{\infty} \frac{\left\lfloor \sqrt{k} \right \rfloor}{k^2}$

Published on 25 Mar 2026 - 12:26

List Question

Compute $\int_0^{\pi/2} x^2\left(\sum_{n=1}^\infty (-1)^{n-1} \cos^n(x)\cos(nx)\right)dx$

Harmonic Series divergence - induction proof

Challenging Integral: $\int_0^\infty\frac{\ln(2+x)\operatorname{Li}_2(-x)}{x(2+x)}dx$

How to compute $\sum_{n=1}^\infty\frac{(-1)^nH_{n/2}}{n^4}$?

How to prove $n \ge 2 {\left ( \sum_{k=1}^n \frac{1}{k} \right)}^2$ for all $n \ge 2$?

Compute $\int_0^1\frac{\tan^{-1}(x)\ln(1+x^2)}{x(1+x)}dx$ using harmonic series

Evaluating $\int_0^{\pi/2} \frac{t \ln (1-\sin{t})}{\sin t} dt$

How to find $I=\int_0^1\frac{\arctan^2x}{1+x}\left(\frac{\ln x}{1-x}+\ln(1+x)\right)dx$

Sum of Scaled Harmonic Numbers

Challenging Sum: compute $\sum_{n=1}^\infty\frac{H_n}{2n+1}\left(\zeta(3)-H_n^{(3)}\right)$

Simplify a sum of harmonic numbers

How to compute $\sum_{n=1}^\infty\frac{(-1)^nH_n}{n^4}$ by real integration only?

An attempt to prove the generalization of $\sum_{n=1}^\infty \frac{(-1)^nH_n}{n^{2a}}$

Compute $\int_0^1\frac{\ln^2(1+x)\operatorname{Li}_2(-x)}{x}dx$

Closed expression for sum $\sum_{k = 1}^{\infty} \frac{\left\lfloor \sqrt{k} \right \rfloor}{k^2}$

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