Question

Prove that $\binom{k+l}{l}$ divides $\binom{2k}{k}\binom{2l}{l}$?

score 196 · Answer 1 · 2026-04-05 13:07:54

196

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Prove that $\binom{k+l}{l}$ divides $\binom{2k}{k}\binom{2l}{l}$?

Published on 05 Apr 2026 - 13:07

score 122 · Answer 2 · 2026-03-31 06:00:54

122

Views

find the value of $\sum_{n=0}^{2016} \frac{\left ( -1 \right )^{n} a_{n}}{4n+1}$ (details inside)

Published on 31 Mar 2026 - 6:00

score 106 · Answer 3 · 2016-09-02 17:57:47

106

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Formula for series of Binomial Coefficients

Published on 02 Sep 2016 - 17:57

score 268 · Answer 4 · 2016-09-02 20:52:16

268

Views

Suppose that $q=\frac{2^n+1}{3}$ is prime then $q$ is the largest factor of $\binom{2^n}{2}-1$

Published on 02 Sep 2016 - 20:52

score 405 · Answer 5 · 2016-09-03 02:11:25

405

Views

A proof of the identity $ \sum_{k = 0}^{n} \frac{(-1)^{k} \binom{n}{k}}{x + k} = \frac{n!}{(x + 0) (x + 1) \cdots (x + n)} $.

Published on 03 Sep 2016 - 2:11

score 143 · Answer 6 · 2026-04-11 14:27:54

143

Views

proof using induction in combinatorics

Published on 11 Apr 2026 - 14:27

score 171 · Answer 7 · 2016-09-04 05:04:23

171

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What is the value of $ \sum\limits_{k=0}^{n-1}\binom {n-k-1}{j-1} \binom {r+k}{j+k}$?

Published on 04 Sep 2016 - 5:04

score 770 · Answer 8 · 2016-09-04 07:22:28

770

Views

Prove binomial identity $\sum^n_{i = 0} \binom i k = \binom{n+1} {k+1}$ by counting the lattice paths

Published on 04 Sep 2016 - 7:22

score 97 · Answer 9 · 2026-04-11 17:26:14

97

Views

A closed formula for the $i$th forward difference of Bézier control points.

Published on 11 Apr 2026 - 17:26

score 123 · Answer 10 · 2026-04-05 13:46:34

123

Views

Proof for $m!(n-m)!|n!$ for $m\leq n$

Published on 05 Apr 2026 - 13:46

score 167 · Answer 11 · 2016-09-04 20:34:51

167

Views

Evaluate this sum: $ \sum_{q=0}^{2n} \binom{p+l-q}{p} \binom{2n}{q}$

Published on 04 Sep 2016 - 20:34

score 36 · Answer 12 · 2026-04-10 04:56:03

36

Views

Am I applying the binomial equation correctly?

Published on 10 Apr 2026 - 4:56

score 1.3k · Answer 13 · 2026-03-31 08:10:51

1.3k

Views

Easy proof: $\binom{n}{k}$ is divisible by $n$ for $\gcd(n,k)=1$

Published on 31 Mar 2026 - 8:10

score 201 · Answer 14 · 2026-03-26 04:53:20

201

Views

Prove that the Bernstein operator preserves function degree. (If $f$ has degree $m$, then $\mathcal{B}(f)$ has degree $m$)

Published on 26 Mar 2026 - 4:53

score 3k · Answer 15 · 2026-04-10 20:59:33

3k

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How to find the number of subsets with different sum in a set?

Published on 10 Apr 2026 - 20:59

List Question

Prove that $\binom{k+l}{l}$ divides $\binom{2k}{k}\binom{2l}{l}$?

find the value of $\sum_{n=0}^{2016} \frac{\left ( -1 \right )^{n} a_{n}}{4n+1}$ (details inside)

Formula for series of Binomial Coefficients

Suppose that $q=\frac{2^n+1}{3}$ is prime then $q$ is the largest factor of $\binom{2^n}{2}-1$

A proof of the identity $ \sum_{k = 0}^{n} \frac{(-1)^{k} \binom{n}{k}}{x + k} = \frac{n!}{(x + 0) (x + 1) \cdots (x + n)} $.

proof using induction in combinatorics

What is the value of $ \sum\limits_{k=0}^{n-1}\binom {n-k-1}{j-1} \binom {r+k}{j+k}$?

Prove binomial identity $\sum^n_{i = 0} \binom i k = \binom{n+1} {k+1}$ by counting the lattice paths

A closed formula for the $i$th forward difference of Bézier control points.

Proof for $m!(n-m)!|n!$ for $m\leq n$

Evaluate this sum: $ \sum_{q=0}^{2n} \binom{p+l-q}{p} \binom{2n}{q}$

Am I applying the binomial equation correctly?

Easy proof: $\binom{n}{k}$ is divisible by $n$ for $\gcd(n,k)=1$

Prove that the Bernstein operator preserves function degree. (If $f$ has degree $m$, then $\mathcal{B}(f)$ has degree $m$)

How to find the number of subsets with different sum in a set?

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