List questions from binomial-coefficients

Published on 05 Oct 2016 - 6:43

173

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Partial Chu-Vandermonde summation $\sum\limits_{i=0}^{k/2-1} {n/4 \choose i}{3n/4 \choose k-i}$

Published on 05 Oct 2016 - 14:00

106

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Prove $\binom km\binom tk=\binom tm\binom{t-m}{t-k}$

Published on 07 Oct 2016 - 3:02

98

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Combinatorics identity

Published on 12 Apr 2026 - 5:02

44

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How to prove the following equivalent using algebraic solution?

Published on 10 Apr 2026 - 17:33

843

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Simplify $\binom{m+n}{2} - \binom{m}{2} - \binom{n}{2}$.

Published on 07 Oct 2016 - 19:30

115

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Sum of Triple Product of Binomial Coefficients with fixed variable sum

Published on 11 Apr 2026 - 14:59

775

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Binomial - Find values of a, b and n

Published on 08 Oct 2016 - 8:16

195

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Sum of series $1+\frac{1}{4}+\frac{1\times3}{4\times8}+\frac{1\times3\times5}{4\times8 \times12}+\cdots$

Published on 08 Oct 2016 - 14:42

650

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Prove a combinatoric sum: $\sum_{j=0}^{k}{{2k-j}\choose{j}}2^j=\frac{1}{3}(1+2^{2k+1})$

Published on 08 Oct 2016 - 15:16

168

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Operations on Binomial coefficients

Published on 12 Apr 2026 - 1:30

339

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Sum of the series $\binom{n}{0}-\binom{n-1}{1}+\binom{n-2}{2}-\binom{n-3}{3}+..........$

Published on 09 Oct 2016 - 16:32

2.8k

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Lemma on switching between mod $p$ and mod $p^2$ or mod $p^3$

Published on 10 Oct 2016 - 0:08

86

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Binomial Coefficient Conjecture

Published on 12 Apr 2026 - 7:06

198

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Binomial Coefficient Odd?

Published on 31 Mar 2026 - 10:34

List Question

Prove that $\binom{2n}{n}>\frac{4n}{n+1}\forall \; n\geq 2, n\in \mathbb{N}$

Partial Chu-Vandermonde summation $\sum\limits_{i=0}^{k/2-1} {n/4 \choose i}{3n/4 \choose k-i}$

Prove $\binom km\binom tk=\binom tm\binom{t-m}{t-k}$

Combinatorics identity

How to prove the following equivalent using algebraic solution?

Simplify $\binom{m+n}{2} - \binom{m}{2} - \binom{n}{2}$.

Sum of Triple Product of Binomial Coefficients with fixed variable sum

Binomial - Find values of a, b and n

Sum of series $1+\frac{1}{4}+\frac{1\times3}{4\times8}+\frac{1\times3\times5}{4\times8 \times12}+\cdots$

Prove a combinatoric sum: $\sum_{j=0}^{k}{{2k-j}\choose{j}}2^j=\frac{1}{3}(1+2^{2k+1})$

Operations on Binomial coefficients

Sum of the series $\binom{n}{0}-\binom{n-1}{1}+\binom{n-2}{2}-\binom{n-3}{3}+..........$

Lemma on switching between mod $p$ and mod $p^2$ or mod $p^3$

Binomial Coefficient Conjecture

Binomial Coefficient Odd?

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