Question

Can $0$ be an element of a harmonic series?

score 436 · Answer 1 · 2020-04-30 07:40:51

436

Views

Can $0$ be an element of a harmonic series?

Published on 30 Apr 2020 - 7:40

score 147 · Answer 2 · 2020-05-01 08:42:24

147

Views

Can I get a bound on $\sum_i x_i$ given a bound on $\sum_i x_i/(1+x_i)$?

Published on 01 May 2020 - 8:42

score 168 · Answer 3 · 2020-05-01 10:18:27

168

Views

Prove that $\sum_{n=2}^{\infty} \frac{(-1)^{n}}{n}\zeta(n) = \gamma$

Published on 01 May 2020 - 10:18

score 142 · Answer 4 · 2020-05-02 10:09:19

142

Views

How to determine bounds on one variable in a system of inequalities?

Published on 02 May 2020 - 10:09

score 218 · Answer 5 · 2020-05-04 06:08:44

218

Views

Convergence of $\sum_{n=1}^{\infty}\frac{(-1)^{T_n+1}}{n},$ where $T_n$ is the $n$th Triangular number

Published on 04 May 2020 - 6:08

score 280 · Answer 6 · 2020-05-07 12:59:55

280

Views

Binomial Euler sums: Evaluate $\sum_{n=1}^\infty\frac1{4^n}\binom{2n}n\frac{H_n^{(s_1)}\cdots H_n^{(s_k)}}{n^s}$

Published on 07 May 2020 - 12:59

score 501 · Answer 7 · 2020-05-09 16:09:26

501

Views

Prove $\sum_{i=1}^{n-1} \left[\frac{n}{i(i+1)} + \frac{n(n-1)}{i(i+1)} (n(H_{n-2} - H_{n-i-1}) - (i-1))) \right] =(n-1)^2$?

Published on 09 May 2020 - 16:09

score 214 · Answer 8 · 2020-05-11 14:37:07

214

Views

How close to an integer can the harmonic series of prime numbers be?

Published on 11 May 2020 - 14:37

score 55 · Answer 9 · 2020-05-11 15:53:10

55

Views

Is there a simpler expression for the sum $\sum_{i=1}^{\infty} \frac{H_{i}}{i+1}$?

Published on 11 May 2020 - 15:53

score 75 · Answer 10 · 2020-05-16 12:28:10

75

Views

Sum of series scaled by the harmonic series

Published on 16 May 2020 - 12:28

score 87 · Answer 11 · 2026-03-25 10:15:35

87

Views

Sum of series with conditional convergence

Published on 25 Mar 2026 - 10:15

score 327 · Answer 12 · 2026-03-25 12:50:15

327

Views

Understanding this property of the digamma function: $\psi(n + \frac{1}{2}) = -\gamma - 2\ln 2 + \sum\limits_{k=1}^n\frac{2}{2k-1}$

Published on 25 Mar 2026 - 12:50

score 184 · Answer 13 · 2020-05-20 05:57:11

184

Views

Sum $\sum_{k=1}^{\infty} \frac{(-1)^{k-1}H_{2k}}{k}$

Published on 20 May 2020 - 5:57

score 239 · Answer 14 · 2026-03-26 21:27:50

239

Views

Compute $\int_0^1 \frac{\text{Li}_2(-x^2)\log (x^2+1)}{x^2+1} \, dx$

Published on 26 Mar 2026 - 21:27

score 134 · Answer 15 · 2020-05-23 19:10:27

134

Views

Prove $\sum_{k=1}^{\infty} \frac{H_{k}^{(2)}}{2^kk} = \frac{5\zeta(3)}{8}$

Published on 23 May 2020 - 19:10

List Question

Can $0$ be an element of a harmonic series?

Can I get a bound on $\sum_i x_i$ given a bound on $\sum_i x_i/(1+x_i)$?

Prove that $\sum_{n=2}^{\infty} \frac{(-1)^{n}}{n}\zeta(n) = \gamma$

How to determine bounds on one variable in a system of inequalities?

Convergence of $\sum_{n=1}^{\infty}\frac{(-1)^{T_n+1}}{n},$ where $T_n$ is the $n$th Triangular number

Binomial Euler sums: Evaluate $\sum_{n=1}^\infty\frac1{4^n}\binom{2n}n\frac{H_n^{(s_1)}\cdots H_n^{(s_k)}}{n^s}$

Prove $\sum_{i=1}^{n-1} \left[\frac{n}{i(i+1)} + \frac{n(n-1)}{i(i+1)} (n(H_{n-2} - H_{n-i-1}) - (i-1))) \right] =(n-1)^2$?

How close to an integer can the harmonic series of prime numbers be?

Is there a simpler expression for the sum $\sum_{i=1}^{\infty} \frac{H_{i}}{i+1}$?

Sum of series scaled by the harmonic series

Sum of series with conditional convergence

Understanding this property of the digamma function: $\psi(n + \frac{1}{2}) = -\gamma - 2\ln 2 + \sum\limits_{k=1}^n\frac{2}{2k-1}$

Sum $\sum_{k=1}^{\infty} \frac{(-1)^{k-1}H_{2k}}{k}$

Compute $\int_0^1 \frac{\text{Li}_2(-x^2)\log (x^2+1)}{x^2+1} \, dx$

Prove $\sum_{k=1}^{\infty} \frac{H_{k}^{(2)}}{2^kk} = \frac{5\zeta(3)}{8}$

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