Question

Sum $\frac{1}{2}\sum_{\substack{n = 1 \\n \text{ odd}}}^{\infty} \sum_{k=0}^n \frac{x^k}{k!} \frac{x^{n-k}}{(n-k)!}$

score 95 · Answer 1 · 2026-03-26 17:53:47

95

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Sum $\frac{1}{2}\sum_{\substack{n = 1 \\n \text{ odd}}}^{\infty} \sum_{k=0}^n \frac{x^k}{k!} \frac{x^{n-k}}{(n-k)!}$

Published on 26 Mar 2026 - 17:53

score 191 · Answer 2 · 2026-04-11 23:21:52

191

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Calculating $\sum_{k=0}^{n}\binom{n}{k}\frac{1}{k+1}$

Published on 11 Apr 2026 - 23:21

score 182 · Answer 3 · 2026-04-13 15:55:33

182

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Proof that $\sum\limits_{n=1}^\infty\frac1{n2^n}=\ln2 $?

Published on 13 Apr 2026 - 15:55

score 504 · Answer 4 · 2026-04-16 13:10:21

504

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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 16 Apr 2026 - 13:10

score 174 · Answer 5 · 2026-05-10 16:07:09

174

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Schur inequality

Published on 10 May 2026 - 16:07

score 55 · Answer 6 · 2026-04-16 17:14:17

55

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prove that $ \frac{\sqrt{m}}{m} \sum_{i=1}^m |x_i| \leq |x| \leq \sum_{i=1}^m |x_i|$

Published on 16 Apr 2026 - 17:14

score 396 · Answer 7 · 2026-03-25 18:53:39

396

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Catalan numbers with unequal opening and closing brackets.

Published on 25 Mar 2026 - 18:53

score 60 · Answer 8 · 2026-03-26 12:32:27

60

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summation for trapezoid

Published on 26 Mar 2026 - 12:32

score 24 · Answer 9 · 2026-04-13 14:34:50

24

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Evaluating this finite sum help

Published on 13 Apr 2026 - 14:34

score 35 · Answer 10 · 2026-04-11 15:34:53

35

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Should the bounds be reversed in this sum?

Published on 11 Apr 2026 - 15:34

score 51 · Answer 11 · 2026-04-12 00:02:05

51

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What is a closed form for this combinatorial sum?

Published on 12 Apr 2026 - 0:02

score 108 · Answer 12 · 2026-05-10 17:09:50

108

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How to find a closed form expression for a multivariate convolution identity?

Published on 10 May 2026 - 17:09

score 49 · Answer 13 · 2026-04-14 22:44:24

49

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Combinatorial proof of $1+2(\sum_{i=0}^n 3^i)=3^{n+1}$

Published on 14 Apr 2026 - 22:44

score 39 · Answer 14 · 2026-04-14 21:01:49

39

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Why the sum$\sum_{n=1}^\infty \left(n^{n^a}-1\right)$ converges when a is strictly less then -1

Published on 14 Apr 2026 - 21:01

score 66 · Answer 15 · 2026-03-25 16:02:39

66

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Summation problem: find k if $\sum_{k=5}^{29} kn-6=1125$

Published on 25 Mar 2026 - 16:02

List Question

Sum $\frac{1}{2}\sum_{\substack{n = 1 \\n \text{ odd}}}^{\infty} \sum_{k=0}^n \frac{x^k}{k!} \frac{x^{n-k}}{(n-k)!}$

Calculating $\sum_{k=0}^{n}\binom{n}{k}\frac{1}{k+1}$

Proof that $\sum\limits_{n=1}^\infty\frac1{n2^n}=\ln2 $?

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

Schur inequality

prove that $ \frac{\sqrt{m}}{m} \sum_{i=1}^m |x_i| \leq |x| \leq \sum_{i=1}^m |x_i|$

Catalan numbers with unequal opening and closing brackets.

summation for trapezoid

Evaluating this finite sum help

Should the bounds be reversed in this sum?

What is a closed form for this combinatorial sum?

How to find a closed form expression for a multivariate convolution identity?

Combinatorial proof of $1+2(\sum_{i=0}^n 3^i)=3^{n+1}$

Why the sum$\sum_{n=1}^\infty \left(n^{n^a}-1\right)$ converges when a is strictly less then -1

Summation problem: find k if $\sum_{k=5}^{29} kn-6=1125$

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