Question

Inequality containing finite sum.

score 66 · Answer 1 · 2014-07-16 05:07:15

66

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Inequality containing finite sum.

Published on 16 Jul 2014 - 5:07

score 765 · Answer 2 · 2026-04-11 12:27:45

765

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How to find sums like $\sum_{k=0}^{39} \binom{200}{5k}$

Published on 11 Apr 2026 - 12:27

score 109 · Answer 3 · 2026-04-13 11:39:13

109

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Evaluating $\sum \sin(ak) x^k / k! $

Published on 13 Apr 2026 - 11:39

score 188 · Answer 4 · 2026-04-14 09:12:01

188

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$\sum_{k=1}^m n-k$ and $\sum_{k=m+1}^{2m} k$

Published on 14 Apr 2026 - 9:12

score 674 · Answer 5 · 2026-04-13 01:17:54

Can you illustrate the use of coordinate-free notations that serve as an alternative to Einstein summation notation with an example?

score 251 · Answer 6 · 2026-04-03 21:46:17

251

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How to solve this elementary induction proof: $\frac{1}{1^2}+ \cdots+\frac{1}{n^2}\le\ 2-\frac{1}{n}$?

Published on 03 Apr 2026 - 21:46

score 181 · Answer 7 · 2026-04-14 06:46:33

181

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Closed form for the sum: $\sum_{n=1}^{\infty}\frac{1}{n(n + 1/3)}$

Published on 14 Apr 2026 - 6:46

score 2.4k · Answer 8 · 2026-04-12 12:15:59

2.4k

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Partial sum of binomial

Published on 12 Apr 2026 - 12:15

score 727 · Answer 9 · 2026-04-04 00:19:42

727

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Prove $(1-x)^{2k+1} \sum\limits_{n\ge 0}\binom{n+k-1}{k}\binom{n+k}{k} x^n = {\sum\limits_{j\ge 0} \binom{k-1}{j-1}\binom{k+1}{j} x^j} $

Published on 04 Apr 2026 - 0:19

score 114 · Answer 10 · 2026-04-12 04:22:51

114

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How to find the value of this summation?

Published on 12 Apr 2026 - 4:22

score 75 · Answer 11 · 2026-04-12 12:06:26

75

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Sum and binomials

Published on 12 Apr 2026 - 12:06

score 405 · Answer 12 · 2014-07-17 16:05:16

405

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What is the closed form for $S=\sum_{n=1}^{\infty} \frac{\sin ({n})}{n!}$?

Published on 17 Jul 2014 - 16:05

score 250 · Answer 13 · 2026-04-03 21:46:39

250

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Prove by induction that $A_k = \sum\limits_{n=2k}^{3k}\binom{3k}{n}\cdot{(\frac{60}{100})}^n\cdot{(\frac{40}{100})}^{3k-n}$ is decreasing

Published on 03 Apr 2026 - 21:46

score 470 · Answer 14 · 2026-04-13 11:11:07

470

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Help with finding the arithmetic mean of all the radii from the center to the edge of an ellipse?

Published on 13 Apr 2026 - 11:11

score 151 · Answer 15 · 2014-07-18 16:45:23

151

Views

The sum of $1^2+7^2+13^2+\cdots+n^2,$ where $ n =1 \mod6 $

Published on 18 Jul 2014 - 16:45

List Question

Inequality containing finite sum.

How to find sums like $\sum_{k=0}^{39} \binom{200}{5k}$

Evaluating $\sum \sin(ak) x^k / k! $

$\sum_{k=1}^m n-k$ and $\sum_{k=m+1}^{2m} k$

Can you illustrate the use of coordinate-free notations that serve as an alternative to Einstein summation notation with an example?

How to solve this elementary induction proof: $\frac{1}{1^2}+ \cdots+\frac{1}{n^2}\le\ 2-\frac{1}{n}$?

Closed form for the sum: $\sum_{n=1}^{\infty}\frac{1}{n(n + 1/3)}$

Partial sum of binomial

Prove $(1-x)^{2k+1} \sum\limits_{n\ge 0}\binom{n+k-1}{k}\binom{n+k}{k} x^n = {\sum\limits_{j\ge 0} \binom{k-1}{j-1}\binom{k+1}{j} x^j} $

How to find the value of this summation?

Sum and binomials

What is the closed form for $S=\sum_{n=1}^{\infty} \frac{\sin ({n})}{n!}$?

Prove by induction that $A_k = \sum\limits_{n=2k}^{3k}\binom{3k}{n}\cdot{(\frac{60}{100})}^n\cdot{(\frac{40}{100})}^{3k-n}$ is decreasing

Help with finding the arithmetic mean of all the radii from the center to the edge of an ellipse?

The sum of $1^2+7^2+13^2+\cdots+n^2,$ where $ n =1 \mod6 $

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