Question

How to evaluate $ \sum_{n=1}^\infty \frac{H_n^{(2)}}{n^3}$

score 149 · Answer 1 · 2026-03-26 23:11:43

149

Views

How to evaluate $ \sum_{n=1}^\infty \frac{H_n^{(2)}}{n^3}$

Published on 26 Mar 2026 - 23:11

score 111 · Answer 2 · 2026-03-26 21:27:42

111

Views

Evaluate $\sum_{n\geq1} \frac{(-1)^{n+1}H_n^2}{(n+1)^2}$.

Published on 26 Mar 2026 - 21:27

score 85 · Answer 3 · 2026-03-26 21:27:14

85

Views

Is there a nice way to represent $\sum_{n=1}^\infty \frac{(-1)^{n+1}H_n}{n+m+1}$?

Published on 26 Mar 2026 - 21:27

score 110 · Answer 4 · 2026-03-26 23:11:45

110

Views

How to compute $\sum_{n=1}^\infty \frac{H_{2n}^2}{n^2}$?

Published on 26 Mar 2026 - 23:11

score 67 · Answer 5 · 2026-03-25 19:04:18

67

Views

Does the green area converge to a known constant when $n\to \infty$?

Published on 25 Mar 2026 - 19:04

score 117 · Answer 6 · 2020-06-22 06:45:41

117

Views

Evaluating the indefinite Harmonic number integral $\int \frac{1-t^n}{1-t} dt$

Published on 22 Jun 2020 - 6:45

score 98 · Answer 7 · 2020-06-23 03:50:03

98

Views

Explanation of part of a particular proof by induction that the harmonic series diverges

Published on 23 Jun 2020 - 3:50

score 78 · Answer 8 · 2020-06-23 23:28:59

78

Views

How to show $\sum_{k=1}^\infty\sum_{n=1}^\infty\frac{H_{n-1}}{n^2(n+k)^2}=\sum_{n=1}^\infty\frac{H_{n-1}^{(2)}}{n^3}$ using series manipulation?

Published on 23 Jun 2020 - 23:28

score 253 · Answer 9 · 2026-03-26 01:11:06

253

Views

Evaluate hypergeometric $_6F_5\left(\{\frac12\}_6;1,\{\frac32\}_4;1\right)$

Published on 26 Mar 2026 - 1:11

score 122 · Answer 10 · 2026-03-25 23:37:02

122

Views

Can these two conjectured relationships between two prime counting functions and the harmonic number function $H(x)$ be proven?

Published on 25 Mar 2026 - 23:37

score 223 · Answer 11 · 2020-06-28 14:56:53

223

Views

Evaluation of double summation

Published on 28 Jun 2020 - 14:56

score 109 · Answer 12 · 2020-07-02 08:18:29

109

Views

If $ 1+ \frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}=\frac{A}{B}$ where $A$ and $B$ are coprime positive integers, then $5\nmid A$ and $5\nmid B$.

Published on 02 Jul 2020 - 8:18

score 256 · Answer 13 · 2026-03-25 22:05:17

256

Views

General method of evaluating $\small\sum_{n\geq 0}\left(\frac{4^n}{(2n+1)\binom{2n}{n}}\right)^2\frac{1}{n+k}$

Published on 25 Mar 2026 - 22:05

score 1.4k · Answer 14 · 2020-07-04 18:42:39

1.4k

Views

Upper bound of $\sum_{k=1}^n \frac{1}{\sqrt{k}}$?

Published on 04 Jul 2020 - 18:42

score 165 · Answer 15 · 2020-07-07 06:53:34

165

Views

How to Evaluate the Sum $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}\left(H_{n}\right)^2}{2n+1}$

Published on 07 Jul 2020 - 6:53

List Question

How to evaluate $ \sum_{n=1}^\infty \frac{H_n^{(2)}}{n^3}$

Evaluate $\sum_{n\geq1} \frac{(-1)^{n+1}H_n^2}{(n+1)^2}$.

Is there a nice way to represent $\sum_{n=1}^\infty \frac{(-1)^{n+1}H_n}{n+m+1}$?

How to compute $\sum_{n=1}^\infty \frac{H_{2n}^2}{n^2}$?

Does the green area converge to a known constant when $n\to \infty$?

Evaluating the indefinite Harmonic number integral $\int \frac{1-t^n}{1-t} dt$

Explanation of part of a particular proof by induction that the harmonic series diverges

How to show $\sum_{k=1}^\infty\sum_{n=1}^\infty\frac{H_{n-1}}{n^2(n+k)^2}=\sum_{n=1}^\infty\frac{H_{n-1}^{(2)}}{n^3}$ using series manipulation?

Evaluate hypergeometric $_6F_5\left(\{\frac12\}_6;1,\{\frac32\}_4;1\right)$

Can these two conjectured relationships between two prime counting functions and the harmonic number function $H(x)$ be proven?

Evaluation of double summation

If $ 1+ \frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}=\frac{A}{B}$ where $A$ and $B$ are coprime positive integers, then $5\nmid A$ and $5\nmid B$.

General method of evaluating $\small\sum_{n\geq 0}\left(\frac{4^n}{(2n+1)\binom{2n}{n}}\right)^2\frac{1}{n+k}$

Upper bound of $\sum_{k=1}^n \frac{1}{\sqrt{k}}$?

How to Evaluate the Sum $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}\left(H_{n}\right)^2}{2n+1}$

Trending Questions

Popular # Hahtags

Popular Questions