Question

Any proof for :Sum of two perfect number never be a perfect number?

score 234 · Answer 1 · 2026-03-20 02:48:53

234

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Any proof for :Sum of two perfect number never be a perfect number?

Published on 20 Mar 2026 - 2:48

score 96 · Answer 2 · 2026-03-25 17:24:13

96

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Evaluating $\sum\limits_{k=0}^n \frac{(-1)^k (4 n - 2 k)!}{k! (2 n - k)! (2 n - 2 k)! (2 n + 2 r + 1 - 2 k)}$

Published on 25 Mar 2026 - 17:24

score 71 · Answer 3 · 2026-03-26 11:01:02

71

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how do I show this :$\sum_{k=0}^{2n }\binom{2n}{k} \sin ((n-k)x)=0$ , for every real $x$ and for every integer $n$?

Published on 26 Mar 2026 - 11:01

score 504 · Answer 4 · 2026-03-23 08:03:09

504

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Proving the Multinomial Theorem--Collapsing Double Sum (Multiple Summation Step)

Published on 23 Mar 2026 - 8:03

score 132 · Answer 5 · 2018-03-31 19:51:46

132

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Sum of $ \sum_{n=2}^{\infty}(-1)^n *\frac{ \ln(n-1)}{n}$

Published on 31 Mar 2018 - 19:51

score 218 · Answer 6 · 2026-03-26 00:58:19

218

Views

Evaluate the sum using derivatives and generating functions

Published on 26 Mar 2026 - 0:58

score 99 · Answer 7 · 2026-03-25 16:06:06

99

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Sum Reduction (Binomial Theorem Related)

Published on 25 Mar 2026 - 16:06

score 77 · Answer 8 · 2018-04-01 18:01:04

77

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Evaluation of ::$S=\frac {9}{15} +\frac {19} {15^2} +\frac {119} {15^3}+\frac {1119} {15^4}\cdots $

Published on 01 Apr 2018 - 18:01

score 2.4k · Answer 9 · 2026-03-26 12:36:38

2.4k

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Proof By Induction: $\sum_{i=1}^n \frac{1}{\sqrt i} > \sqrt n$

Published on 26 Mar 2026 - 12:36

score 38 · Answer 10 · 2026-03-25 09:33:41

38

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Can we find Convolution Sum Boundaries without graphical plot (Analytic Method)?

Published on 25 Mar 2026 - 9:33

score 177 · Answer 11 · 2026-03-26 01:04:42

177

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Why do expressions of the form $\sum\limits^\infty_{n=1} \frac{n^k}{3^n}$ sum 'nicely'?

Published on 26 Mar 2026 - 1:04

score 859 · Answer 12 · 2018-04-02 14:50:16

859

Views

Applying the ratio test and uniform convergence

Published on 02 Apr 2018 - 14:50

score 146 · Answer 13 · 2018-04-02 18:20:35

146

Views

Show that $\sum_{k=1}^{\infty}\frac{2^{-k}}{k}=\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{k}$ without evaluating either sum

Published on 02 Apr 2018 - 18:20

score 176 · Answer 14 · 2026-03-17 10:26:20

176

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Is there a close form for $g(a,b,n)=\sum\limits_{k=0}^{n}\binom{n}{k}\frac{1}{ak+b}$?

Published on 17 Mar 2026 - 10:26

score 177 · Answer 15 · 2018-04-03 01:45:33

177

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Is there a way to sum $\sum_{n=1}^{\infty}\left[ \frac{y}{n} - \tan^{-1}\left( \frac{y}{n} \right)\right]$

Published on 03 Apr 2018 - 1:45

List Question

Any proof for :Sum of two perfect number never be a perfect number?

Evaluating $\sum\limits_{k=0}^n \frac{(-1)^k (4 n - 2 k)!}{k! (2 n - k)! (2 n - 2 k)! (2 n + 2 r + 1 - 2 k)}$

how do I show this :$\sum_{k=0}^{2n }\binom{2n}{k} \sin ((n-k)x)=0$ , for every real $x$ and for every integer $n$?

Proving the Multinomial Theorem--Collapsing Double Sum (Multiple Summation Step)

Sum of $ \sum_{n=2}^{\infty}(-1)^n *\frac{ \ln(n-1)}{n}$

Evaluate the sum using derivatives and generating functions

Sum Reduction (Binomial Theorem Related)

Evaluation of ::$S=\frac {9}{15} +\frac {19} {15^2} +\frac {119} {15^3}+\frac {1119} {15^4}\cdots $

Proof By Induction: $\sum_{i=1}^n \frac{1}{\sqrt i} > \sqrt n$

Can we find Convolution Sum Boundaries without graphical plot (Analytic Method)?

Why do expressions of the form $\sum\limits^\infty_{n=1} \frac{n^k}{3^n}$ sum 'nicely'?

Applying the ratio test and uniform convergence

Show that $\sum_{k=1}^{\infty}\frac{2^{-k}}{k}=\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{k}$ without evaluating either sum

Is there a close form for $g(a,b,n)=\sum\limits_{k=0}^{n}\binom{n}{k}\frac{1}{ak+b}$?

Is there a way to sum $\sum_{n=1}^{\infty}\left[ \frac{y}{n} - \tan^{-1}\left( \frac{y}{n} \right)\right]$

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