Question

Find triple summation rel in a closed form $S=\sum_{n=1}^{\infty}\sum_{m=1}^{n}\sum_{k=1}^{m}\frac{1}{(n+1)(k+1)(m+1)nmk}$

score 243 · Answer 1 · 2026-03-27 10:12:08

243

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Find triple summation rel in a closed form $S=\sum_{n=1}^{\infty}\sum_{m=1}^{n}\sum_{k=1}^{m}\frac{1}{(n+1)(k+1)(m+1)nmk}$

Published on 27 Mar 2026 - 10:12

score 112 · Answer 2 · 2019-07-16 01:38:20

112

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Closed-form expressions for nth composition of a function

Published on 16 Jul 2019 - 1:38

score 243 · Answer 3 · 2026-03-26 02:57:54

243

Views

Express $\sum_{j=1}^{n}\sum_{i=1}^{n} \frac{1}{i(i+j)}$ in terms of harmonic numbers

Published on 26 Mar 2026 - 2:57

score 72 · Answer 4 · 2026-03-27 10:09:33

72

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some identity of summation and generalization

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score 189 · Answer 5 · 2026-04-08 11:13:34

189

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score 199 · Answer 6 · 2026-03-25 14:25:19

199

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How to find Sum of Sum of Partial Harmonic Series: $\sum_{b=1}^{m} \sum_{k=1}^{b} \frac{1}{k} $?

Published on 25 Mar 2026 - 14:25

score 1k · Answer 7 · 2019-07-17 01:02:04

1k

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How to find the consecutive odd numbers that sum to a given odd number

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score 70 · Answer 8 · 2019-07-17 17:39:15

70

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Infinite Factorial Sum

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score 765 · Answer 9 · 2026-04-02 18:39:18

765

Views

Does a general formula for $\sum_{r=1}^{n}r^k$ proof exist?

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score 163 · Answer 10 · 2026-03-25 07:44:43

163

Views

Computing $\frac{\sin(3)}{\cos(0)\cos(3)}+\frac{\sin(3)}{\cos(3)\cos(6)} +\cdots+\frac{\sin(3)}{\cos(42)\cos(45)}$

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score 84 · Answer 11 · 2026-03-29 13:29:06

84

Views

On the irrationality of $\sum_{n=1}^{\infty} b^{-a_n} $

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score 181 · Answer 12 · 2019-07-18 09:29:59

181

Views

Bound on the tail of sum of inverse squares

Published on 18 Jul 2019 - 9:29

score 92 · Answer 13 · 2026-04-06 12:56:34

92

Views

For which pairs $(a/b)$ is $f(a,b)$ defined?

Published on 06 Apr 2026 - 12:56

score 299 · Answer 14 · 2026-03-27 04:35:13

299

Views

Are there infinitely many zeroes of $\sum_{r = 1}^{n-1} \mu(r)\gcd(n,r) $?

Published on 27 Mar 2026 - 4:35

score 168 · Answer 15 · 2019-07-18 17:19:51

168

Views

Sum of an Infinite Sequence

Published on 18 Jul 2019 - 17:19

List Question

Find triple summation rel in a closed form $S=\sum_{n=1}^{\infty}\sum_{m=1}^{n}\sum_{k=1}^{m}\frac{1}{(n+1)(k+1)(m+1)nmk}$

Closed-form expressions for nth composition of a function

Express $\sum_{j=1}^{n}\sum_{i=1}^{n} \frac{1}{i(i+j)}$ in terms of harmonic numbers

some identity of summation and generalization

Higher powers in the discrete Plancherel theorem

How to find Sum of Sum of Partial Harmonic Series: $\sum_{b=1}^{m} \sum_{k=1}^{b} \frac{1}{k} $?

How to find the consecutive odd numbers that sum to a given odd number

Infinite Factorial Sum

Does a general formula for $\sum_{r=1}^{n}r^k$ proof exist?

Computing $\frac{\sin(3)}{\cos(0)\cos(3)}+\frac{\sin(3)}{\cos(3)\cos(6)} +\cdots+\frac{\sin(3)}{\cos(42)\cos(45)}$

On the irrationality of $\sum_{n=1}^{\infty} b^{-a_n} $

Bound on the tail of sum of inverse squares

For which pairs $(a/b)$ is $f(a,b)$ defined?

Are there infinitely many zeroes of $\sum_{r = 1}^{n-1} \mu(r)\gcd(n,r) $?

Sum of an Infinite Sequence

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