List questions from binomial-coefficients

Published on 21 Oct 2014 - 23:17

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Prove a theorem in combinatorics

Published on 21 Oct 2014 - 23:31

322

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Compute $\sum_{k=0}^{n}\frac{1}{\binom{n}{k}}$

Published on 22 Oct 2014 - 13:45

57

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Analyzing a coin tossing game with cheating

Published on 22 Oct 2014 - 14:05

803

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Proving that polynomials with rational coefficients have integer roots

Published on 22 Oct 2014 - 22:57

124

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Chance of winning in a raffle

Published on 23 Oct 2014 - 5:50

343

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Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$

Published on 28 Mar 2026 - 1:08

5.5k

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Show that ${n \choose k}{k \choose m} = {n \choose m}{n-m \choose k-m}$

Published on 24 Oct 2014 - 18:37

195

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Sum of coefficients in binomial theory.

Published on 24 Oct 2014 - 22:24

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Harmonic number identity

Published on 25 Mar 2026 - 21:00

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Relation among numbers in a triangle like tartaglia:

Published on 26 Oct 2014 - 16:48

191

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Summation using cdf of binomial distribution

Published on 27 Oct 2014 - 4:53

53

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How find this binomial-coefficients sum $\sum_{k_{1}+k_{2}+\cdots+k_{d}=n}\binom{n}{k_{1},k_{2},\cdots,k_{d}}^2$

Published on 27 Oct 2014 - 16:30

537

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How to prove that $\sum_{k=0}^n\cos(k\pi)\binom{n}{k}=0$?

Published on 27 Oct 2014 - 20:18

96

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$\sum_{k=0}^n\binom nk x^k=\sum_{k=0}^n\binom nk x^{n-k}.$

Published on 27 Oct 2014 - 20:59

List Question

Calculate limit involving binomial coefficient

Prove a theorem in combinatorics

Compute $\sum_{k=0}^{n}\frac{1}{\binom{n}{k}}$

Analyzing a coin tossing game with cheating

Proving that polynomials with rational coefficients have integer roots

Chance of winning in a raffle

Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$

Show that ${n \choose k}{k \choose m} = {n \choose m}{n-m \choose k-m}$

Sum of coefficients in binomial theory.

Harmonic number identity

Relation among numbers in a triangle like tartaglia:

Summation using cdf of binomial distribution

How find this binomial-coefficients sum $\sum_{k_{1}+k_{2}+\cdots+k_{d}=n}\binom{n}{k_{1},k_{2},\cdots,k_{d}}^2$

How to prove that $\sum_{k=0}^n\cos(k\pi)\binom{n}{k}=0$?

$\sum_{k=0}^n\binom nk x^k=\sum_{k=0}^n\binom nk x^{n-k}.$

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