List questions from binomial-coefficients

Published on 26 Mar 2026 - 11:06

112

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Sum of a part of binomial expansion.

Published on 17 Mar 2019 - 20:15

51

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Why $\sum_{i = j}^\infty\frac{i!}{(i-j)!\cdot j!}\cdot k^{i-j}\cdot (1-k)^j = 1/(1-k)$?

Published on 18 Mar 2019 - 12:53

155

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Proof that binomial $\binom{n}{k}$ is an integer for $0>n\in\mathbb{Z}$

Published on 18 Mar 2019 - 14:10

169

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Binomial series expansion of a trinomial?

Published on 25 Mar 2026 - 4:39

49

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If $g\left(x-3\right)=x^4$ what is $g\left(x\right)$?

Published on 18 Mar 2019 - 20:46

51

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Is $\binom{2^{n}}{j}\cdot 2^{2^{n}-j}$ divisible by $2^{n}$ for all $0 \leq j < 2^{n}$?

Published on 27 Mar 2026 - 22:52

166

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A sum of a product of binomial coefficients

Published on 19 Mar 2019 - 19:03

111

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Coefficients of $(1+x+x^2)^{2018}$

Published on 19 Mar 2019 - 21:24

55

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proving complex Binomial Identity

Published on 20 Mar 2019 - 2:04

103

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Recursion series with two variable indices $u_{n,k} = u_{n-1,k} + u_{n-2,k-1}$

Published on 27 Mar 2026 - 1:44

129

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Prove $\sum_{i=0}^n\binom{m+i}{i}=\binom{m+n+1}{n}$ (another Hockey-Stick Identity?)

Published on 22 Mar 2019 - 3:15

764

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Showing $\sum_{k=0}^{n} {n \choose k}\frac{{(-1)}^k}{n+k+1}$ is positive

Published on 25 Mar 2026 - 6:24

223

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Estimation of a geometric distribution's parameter by the reciprocal of the sample mean

Published on 27 Mar 2026 - 15:19

174

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Combinatorial Proof (Argument) for $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^{k} \binom{n-1-j}{k-j} 2^j$

Published on 27 Mar 2026 - 13:42

List Question

Series limit involving Binomial coefficients

Sum of a part of binomial expansion.

Why $\sum_{i = j}^\infty\frac{i!}{(i-j)!\cdot j!}\cdot k^{i-j}\cdot (1-k)^j = 1/(1-k)$?

Proof that binomial $\binom{n}{k}$ is an integer for $0>n\in\mathbb{Z}$

Binomial series expansion of a trinomial?

If $g\left(x-3\right)=x^4$ what is $g\left(x\right)$?

Is $\binom{2^{n}}{j}\cdot 2^{2^{n}-j}$ divisible by $2^{n}$ for all $0 \leq j < 2^{n}$?

A sum of a product of binomial coefficients

Coefficients of $(1+x+x^2)^{2018}$

proving complex Binomial Identity

Recursion series with two variable indices $u_{n,k} = u_{n-1,k} + u_{n-2,k-1}$

Prove $\sum_{i=0}^n\binom{m+i}{i}=\binom{m+n+1}{n}$ (another Hockey-Stick Identity?)

Showing $\sum_{k=0}^{n} {n \choose k}\frac{{(-1)}^k}{n+k+1}$ is positive

Estimation of a geometric distribution's parameter by the reciprocal of the sample mean

Combinatorial Proof (Argument) for $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^{k} \binom{n-1-j}{k-j} 2^j$

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