List questions from binomial-coefficients

Published on 13 Mar 2026 - 11:36

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A proof in combinatorics (prove by any method)

Published on 13 Mar 2026 - 2:04

80

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If $P_r$ the coefficient of $x^r$ in the expansion of $(1+x)^2 \left(1+\frac{x}{2}\right)^2 \left(1+\frac{x}{2^2}\right)^2 \cdots$

Published on 12 Mar 2026 - 23:43

826

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Prove the following by two different methods, one combinatorial and one algebraic

Published on 13 Mar 2026 - 8:32

86

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Solving the following equation with imaginary roots

Published on 12 Mar 2026 - 22:26

416

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Identity involving binomial coefficients

Published on 13 Mar 2026 - 0:41

80

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Why is this binomial equation not an identity between polynomials?

Published on 13 Mar 2026 - 13:56

93

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Find $\sum_{k=0}^{n}4^k \binom{n}{k}$

Published on 12 Mar 2026 - 23:33

233

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odd property of Eulerian numbers

Published on 22 Mar 2026 - 2:43

194

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prove the following algebraically $\left( \begin{array}{c} 2n \\ 2\ \end{array} \right) = 2 \left( \begin{array}{c} n \\ 2\ \end{array} \right) + n^2$

Published on 13 Mar 2026 - 14:51

185

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Another (complicated?) summation identity with binomial coefficients

Published on 12 Mar 2026 - 23:20

54

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Summation using Complex Numbers

Published on 13 Mar 2026 - 5:59

44

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How to get $[z^n]\displaystyle\frac{z^k}{(1-z)^k} = {n-1 \choose k-1}?$

Published on 12 Mar 2026 - 19:32

73

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Binomial Notation Expansion

Published on 13 Mar 2026 - 8:50

172

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Algebraically prove that $\sum\limits_{k=0}^n {n+k \choose n}\mathrm{2}^{n-k} = 1/2 \cdot \mathrm{2}^{2n+1}$

Published on 12 Mar 2026 - 16:26

List Question

Divisiblity of binomial coefficients

A proof in combinatorics (prove by any method)

If $P_r$ the coefficient of $x^r$ in the expansion of $(1+x)^2 \left(1+\frac{x}{2}\right)^2 \left(1+\frac{x}{2^2}\right)^2 \cdots$

Prove the following by two different methods, one combinatorial and one algebraic

Solving the following equation with imaginary roots

Identity involving binomial coefficients

Why is this binomial equation not an identity between polynomials?

Find $\sum_{k=0}^{n}4^k \binom{n}{k}$

odd property of Eulerian numbers

prove the following algebraically $\left( \begin{array}{c} 2n \\ 2\ \end{array} \right) = 2 \left( \begin{array}{c} n \\ 2\ \end{array} \right) + n^2$

Another (complicated?) summation identity with binomial coefficients

Summation using Complex Numbers

How to get $[z^n]\displaystyle\frac{z^k}{(1-z)^k} = {n-1 \choose k-1}?$

Binomial Notation Expansion

Algebraically prove that $\sum\limits_{k=0}^n {n+k \choose n}\mathrm{2}^{n-k} = 1/2 \cdot \mathrm{2}^{2n+1}$

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