List questions from binomial-theorem

Published on 24 Mar 2026 - 22:50

36

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Binomial Expansion based on equation for evaluation

Published on 10 Mar 2019 - 22:36

59

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Closed form of the sum of two binomial expansions

Published on 15 Mar 2019 - 19:57

103

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$x^{2}+x+1$ is a factor of $(x+1)^{n} - x^{n} - 1$, whenever

Published on 16 Mar 2019 - 11:24

169

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Binomial series expansion of a trinomial?

Published on 25 Mar 2026 - 4:39

650

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Domain limitations on generating function for Legendre polynomials

Published on 23 Feb 2026 - 4:34

162

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Show that $\sum_{r=0}^{n} \binom{n}{r} r p^r q^{n-r} = np$, given $p+q=1$

Published on 22 Mar 2019 - 8:59

5.4k

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Show that $\lim [(2n)^\frac{1}{n})] = 1$

Published on 23 Mar 2019 - 19:50

173

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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 24 Mar 2019 - 4:56

117

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Find $a^3+b^3+c^3-3abc$ (binomial theorem)

Published on 25 Mar 2019 - 14:25

98

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Combinatorial proof for $\sum_{i=k}^n (2i-k) \binom{i-1}{k-1}^2 = k \binom{n}{k}^2$

Published on 26 Mar 2019 - 10:24

81

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strange binomial coefficient identity

Published on 27 Mar 2019 - 3:23

47

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Why is this equality with sums and monomials true?

Published on 27 Mar 2019 - 18:54

1k

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Proving $\sum_{m=0}^n\binom{n}{m}^2 \binom{m}{n-k}=\binom{n}{k}\binom{n+k}{k}$

Published on 30 Mar 2019 - 9:24

64

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Proof of the following combinatorial identity

Published on 30 Mar 2019 - 20:26

List Question

Newtons Binomial Theorem identity

Binomial Expansion based on equation for evaluation

Closed form of the sum of two binomial expansions

$x^{2}+x+1$ is a factor of $(x+1)^{n} - x^{n} - 1$, whenever

Binomial series expansion of a trinomial?

Domain limitations on generating function for Legendre polynomials

Show that $\sum_{r=0}^{n} \binom{n}{r} r p^r q^{n-r} = np$, given $p+q=1$

Show that $\lim [(2n)^\frac{1}{n})] = 1$

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

Find $a^3+b^3+c^3-3abc$ (binomial theorem)

Combinatorial proof for $\sum_{i=k}^n (2i-k) \binom{i-1}{k-1}^2 = k \binom{n}{k}^2$

strange binomial coefficient identity

Why is this equality with sums and monomials true?

Proving $\sum_{m=0}^n\binom{n}{m}^2 \binom{m}{n-k}=\binom{n}{k}\binom{n+k}{k}$

Proof of the following combinatorial identity

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