Question

Solve $\frac{1}{x} + \frac{1}{x+a} + \frac{1}{x+2a} + \cdots = b.$

score 105 · Answer 1 · 2017-06-13 19:56:13

105

Views

Solve $\frac{1}{x} + \frac{1}{x+a} + \frac{1}{x+2a} + \cdots = b.$

Published on 13 Jun 2017 - 19:56

score 127 · Answer 2 · 2017-06-14 12:37:19

127

Views

Generating function for cubes of Harmonic numbers I

Published on 14 Jun 2017 - 12:37

score 560 · Answer 3 · 2017-06-23 14:47:22

560

Views

Elementary way to calculate the series $\sum\limits_{n=1}^{\infty}\frac{H_n}{n2^n}$

Published on 23 Jun 2017 - 14:47

score 776 · Answer 4 · 2026-03-28 03:27:39

776

Views

Closed form for ${\large\int}_0^1\frac{\ln^4(1+x)\ln x}x \, dx$

Published on 28 Mar 2026 - 3:27

score 103 · Answer 5 · 2026-03-27 04:23:55

103

Views

Prove that $\sum_{n=1}^\infty\frac{\mu(n)}{n}H_n\sum_{k=n+1}^\infty\frac{\mu(k)}{k^2}$ is convergent

Published on 27 Mar 2026 - 4:23

score 3k · Answer 6 · 2017-07-21 08:57:34

3k

Views

The limit of $u_n=\sum_{i=1}^n\frac{1}{i}$.

Published on 21 Jul 2017 - 8:57

score 114 · Answer 7 · 2017-07-28 08:51:22

114

Views

Is there a simple description for $\sum_{n=1}^{\infty}\frac{1}{p_n} \to \infty$?

Published on 28 Jul 2017 - 8:51

score 971 · Answer 8 · 2017-07-28 18:42:20

971

Views

Proving that $~\sum\limits_{k=2}^{\infty}\frac{(-1)^k}{k^2}~H_k~H_{k-1}=\frac{3}{16}~\zeta(4)$

Published on 28 Jul 2017 - 18:42

score 203 · Answer 9 · 2017-08-06 07:51:48

203

Views

Inequality $\sum\limits_{k=1}^n \frac{1}{n+k} \le \frac{3}{4}$

Published on 06 Aug 2017 - 7:51

score 1.3k · Answer 10 · 2017-08-19 14:22:16

1.3k

Views

A closed form of $\sum_{n=1}^\infty\left[ H_n^2-\left(\ln n+\gamma+\frac1{2n} \right)^2\right]$

Published on 19 Aug 2017 - 14:22

score 143 · Answer 11 · 2017-08-28 15:42:16

143

Views

The Harmonic Logarithm and its relation to the Prime Number Theorem

Published on 28 Aug 2017 - 15:42

score 480 · Answer 12 · 2026-03-28 03:27:26

480

Views

Integral involving Dilogarithm $\int_{1/2}^{1} \frac{\mathrm{Li}_{2}\left(x\right)\ln\left(2x - 1\right)}{x}\,\mathrm{d}x$

Published on 28 Mar 2026 - 3:27

score 48 · Answer 13 · 2017-08-31 03:55:32

48

Views

Prove the equalities

Published on 31 Aug 2017 - 3:55

score 261 · Answer 14 · 2017-09-03 21:07:46

261

Views

Is this sum $\sum_{k=0}^{n}{n\choose k}\sum_{i=0}^{k}(-1)^i{k\choose i}H_{n+k-i}=H_{2n}$ correct?

Published on 03 Sep 2017 - 21:07

score 494 · Answer 15 · 2026-03-26 15:42:41

494

Views

Why does $(\sum_{i=1}^x \frac{1}{i}) - \ln(x+\frac{1}{2})$ converge to $\gamma$ a lot faster than $(\sum_{i=1}^x \frac{1}{i}) - \ln(x)$

Published on 26 Mar 2026 - 15:42

List Question

Solve $\frac{1}{x} + \frac{1}{x+a} + \frac{1}{x+2a} + \cdots = b.$

Generating function for cubes of Harmonic numbers I

Elementary way to calculate the series $\sum\limits_{n=1}^{\infty}\frac{H_n}{n2^n}$

Closed form for ${\large\int}_0^1\frac{\ln^4(1+x)\ln x}x \, dx$

Prove that $\sum_{n=1}^\infty\frac{\mu(n)}{n}H_n\sum_{k=n+1}^\infty\frac{\mu(k)}{k^2}$ is convergent

The limit of $u_n=\sum_{i=1}^n\frac{1}{i}$.

Is there a simple description for $\sum_{n=1}^{\infty}\frac{1}{p_n} \to \infty$?

Proving that $~\sum\limits_{k=2}^{\infty}\frac{(-1)^k}{k^2}~H_k~H_{k-1}=\frac{3}{16}~\zeta(4)$

Inequality $\sum\limits_{k=1}^n \frac{1}{n+k} \le \frac{3}{4}$

A closed form of $\sum_{n=1}^\infty\left[ H_n^2-\left(\ln n+\gamma+\frac1{2n} \right)^2\right]$

The Harmonic Logarithm and its relation to the Prime Number Theorem

Integral involving Dilogarithm $\int_{1/2}^{1} \frac{\mathrm{Li}_{2}\left(x\right)\ln\left(2x - 1\right)}{x}\,\mathrm{d}x$

Prove the equalities

Is this sum $\sum_{k=0}^{n}{n\choose k}\sum_{i=0}^{k}(-1)^i{k\choose i}H_{n+k-i}=H_{2n}$ correct?

Why does $(\sum_{i=1}^x \frac{1}{i}) - \ln(x+\frac{1}{2})$ converge to $\gamma$ a lot faster than $(\sum_{i=1}^x \frac{1}{i}) - \ln(x)$

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