List questions from binomial-theorem

108

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Prove $\binom{n}{0}$ + $\binom{n}{2}$ + $\binom{n}{4} + ...+\binom{n}{n-1}=\binom{n}{1}+\binom{n}{3}+\binom{n}{5}+...+\binom{n}{n}$

Published on 05 Oct 2022 - 20:55

157

Views

$\binom{n+1}{2} + 2 \left ( \binom{2}{2} + \binom{3}{2} + \dots + \binom{n}{2} \right ) = 1^2+2^2+\dots+n^2.$

Published on 23 Feb 2026 - 12:33

174

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Find the last $2$ digits of $3^{2024}$ using binomial expansion

Published on 07 Oct 2022 - 12:55

65

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Equal coefficients in binomial expansions

Published on 11 Oct 2022 - 8:43

50

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Show with the help of binomial theorem that these two equations are equal?

Published on 21 Oct 2022 - 9:48

57

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Binomial formula for matrix $(\mathbf{I}+\mathbf{A})^{-1/2}$.

Published on 23 Oct 2022 - 14:24

151

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Combinatorics proof of Abel's binomial theorem

Published on 01 Apr 2026 - 2:46

53

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Binomial collisions algorithm

Published on 25 Mar 2026 - 18:43

47

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Prove that the next integer to $(\sqrt3+1)^{2n}$ is $(\sqrt3+1)^{2n}+(\sqrt3-1)^{2n}$

Published on 07 Nov 2022 - 17:39

619

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Double summation over binomial coefficients

Published on 09 Nov 2022 - 17:37

88

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Binomial theorem-respecting polynomials

Published on 13 Nov 2022 - 14:29

205

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Probability of flipping four coins

Published on 05 Apr 2026 - 17:10

333

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Which number is larger? Using Binomial Theorem

Published on 16 Nov 2022 - 13:31

218

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$\binom{54}{5}+\binom{49}{5}+\binom{44}{5}+\cdots+\binom{9}{5}$

Published on 16 Nov 2022 - 13:43

107

Views

About a sum with a combinatorial coefficient

Published on 16 Nov 2022 - 14:57

List Question

Prove $\binom{n}{0}$ + $\binom{n}{2}$ + $\binom{n}{4} + ...+\binom{n}{n-1}=\binom{n}{1}+\binom{n}{3}+\binom{n}{5}+...+\binom{n}{n}$

$\binom{n+1}{2} + 2 \left ( \binom{2}{2} + \binom{3}{2} + \dots + \binom{n}{2} \right ) = 1^2+2^2+\dots+n^2.$

Find the last $2$ digits of $3^{2024}$ using binomial expansion

Equal coefficients in binomial expansions

Show with the help of binomial theorem that these two equations are equal?

Binomial formula for matrix $(\mathbf{I}+\mathbf{A})^{-1/2}$.

Combinatorics proof of Abel's binomial theorem

Binomial collisions algorithm

Prove that the next integer to $(\sqrt3+1)^{2n}$ is $(\sqrt3+1)^{2n}+(\sqrt3-1)^{2n}$

Double summation over binomial coefficients

Binomial theorem-respecting polynomials

Probability of flipping four coins

Which number is larger? Using Binomial Theorem

$\binom{54}{5}+\binom{49}{5}+\binom{44}{5}+\cdots+\binom{9}{5}$

About a sum with a combinatorial coefficient

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