Question

Closed form of finite Euler sum $\sum_{k=1}^n \frac{ H_{k}}{(2k+1)}$

score 403 · Answer 1 · 2018-09-09 00:08:27

403

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Closed form of finite Euler sum $\sum_{k=1}^n \frac{ H_{k}}{(2k+1)}$

Published on 09 Sep 2018 - 0:08

score 1.2k · Answer 2 · 2018-09-22 10:45:08

1.2k

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(Combinatorial?) Proof of the identity $\sum_{k=1}^n \frac {(-1)^k}{k\,(k+1)}\binom nk = \frac 12 + \frac 13 + \dots + \frac 1{n+1}$?

Published on 22 Sep 2018 - 10:45

score 123 · Answer 3 · 2018-10-08 17:29:07

123

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Why can't the divergence of the harmonic series be resolved?

Published on 08 Oct 2018 - 17:29

score 59 · Answer 4 · 2018-10-16 01:41:43

59

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Question on the difference between harmonic series.

Published on 16 Oct 2018 - 1:41

score 93 · Answer 5 · 2018-10-24 00:23:27

93

Views

A very strict inequality for $\ln n$ and $H_{n-1}$, with $n>2$, searching for proof

Published on 24 Oct 2018 - 0:23

score 93 · Answer 6 · 2018-10-29 12:10:56

93

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Number of primes vs harmonic series

Published on 29 Oct 2018 - 12:10

score 1.3k · Answer 7 · 2026-03-24 16:02:38

1.3k

Views

Sum to n terms of the harmonic series

Published on 24 Mar 2026 - 16:02

score 92 · Answer 8 · 2018-11-01 18:44:05

92

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Express $\sum_{n=1}^{\infty} \dfrac1{\prod_{k=1}^m (n+a_k)} $ as a finite sum.

Published on 01 Nov 2018 - 18:44

score 226 · Answer 9 · 2018-11-08 01:02:51

226

Views

Concrete Mathematics: Quicksort analysis

Published on 08 Nov 2018 - 1:02

score 408 · Answer 10 · 2026-03-19 18:48:19

408

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Can $\sum_{n=1}^\infty\frac{H_{2n}}{(2n)^3}$, with $H_n$ the $n$-th harmonic number, be written in terms of $\zeta$ values?

Published on 19 Mar 2026 - 18:48

score 476 · Answer 11 · 2018-11-12 04:32:10

476

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Verify my proof for "For every $n, q$, where $n,q \in Z^+, n\geq 2, \sum_{i=1}^n\frac1n\neq q$". [$n^{th}$ harmonic number is never an integer]

Published on 12 Nov 2018 - 4:32

score 131 · Answer 12 · 2018-11-14 16:53:59

131

Views

Find a reordering of the alternating harmonic sequence such that the limit of the partial sums is $\infty$.

Published on 14 Nov 2018 - 16:53

score 114 · Answer 13 · 2018-11-15 22:23:44

114

Views

holomorphic functions, roots of unity and harmonic numbers

Published on 15 Nov 2018 - 22:23

score 260 · Answer 14 · 2018-11-16 16:22:35

260

Views

Combinatorics: Number of permutations from $1$ to $60$, with cyclic permutation of length $l > 30$

Published on 16 Nov 2018 - 16:22

score 315 · Answer 15 · 2018-11-20 17:08:50

315

Views

Prove $\sum_{k=1}^{\infty}\frac{(-1)^k}{(2k+1)^2}(2H_{2k}+H_k)=\frac{\pi^3}{32}-2G\ln2$

Published on 20 Nov 2018 - 17:08

List Question

Closed form of finite Euler sum $\sum_{k=1}^n \frac{ H_{k}}{(2k+1)}$

(Combinatorial?) Proof of the identity $\sum_{k=1}^n \frac {(-1)^k}{k\,(k+1)}\binom nk = \frac 12 + \frac 13 + \dots + \frac 1{n+1}$?

Why can't the divergence of the harmonic series be resolved?

Question on the difference between harmonic series.

A very strict inequality for $\ln n$ and $H_{n-1}$, with $n>2$, searching for proof

Number of primes vs harmonic series

Sum to n terms of the harmonic series

Express $\sum_{n=1}^{\infty} \dfrac1{\prod_{k=1}^m (n+a_k)} $ as a finite sum.

Concrete Mathematics: Quicksort analysis

Can $\sum_{n=1}^\infty\frac{H_{2n}}{(2n)^3}$, with $H_n$ the $n$-th harmonic number, be written in terms of $\zeta$ values?

Verify my proof for "For every $n, q$, where $n,q \in Z^+, n\geq 2, \sum_{i=1}^n\frac1n\neq q$". [$n^{th}$ harmonic number is never an integer]

Find a reordering of the alternating harmonic sequence such that the limit of the partial sums is $\infty$.

holomorphic functions, roots of unity and harmonic numbers

Combinatorics: Number of permutations from $1$ to $60$, with cyclic permutation of length $l > 30$

Prove $\sum_{k=1}^{\infty}\frac{(-1)^k}{(2k+1)^2}(2H_{2k}+H_k)=\frac{\pi^3}{32}-2G\ln2$

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