List questions from binomial-coefficients

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Differentiation and Binomial

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Problem 6.1.20 Part B From The Arts and Crafts of Problem Solving

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limit of the binomial distribution

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Problem 6.1.26 From The Arts and Crafts of Problem Solving

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Proof of identity $\sum\limits_{k=0}^n \binom{n}{k}\binom{2k}{k}\frac{(-1)^k}{2^{2k}}=2^{-2n}\binom{2n}{n}$

Published on 25 Mar 2026 - 5:54

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Taylor expansion of $\ln(1+\sqrt{1-x})$

Published on 25 Mar 2026 - 14:24

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I want to compute this thing $\sum_{k=0}^{n}{\binom{n}{k}\frac{1}{2k+1}}$ without a dropped induction.

Published on 25 Mar 2026 - 15:20

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Combinatorial proof of $\sum_{k=0}^p {p \choose k}^2 {{n+2p-k}\choose {2p}} = {{n+p} \choose p}^2$

Published on 25 Mar 2026 - 22:05

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Sum of coefficients of even powers of x in $(1+x)^5 (1+x^2)^5$?

Published on 25 Mar 2026 - 22:05

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How is $ C_0^n+\frac{1}{2}(C_0^n-C_1^n)+\frac{1}{3}(C_0^n-C_1^n+C_2^n)+.. =C_0^{n-1}+\frac{1}{2}C_1^{n-1}(-1)+\frac{1}{3}C_2^{n-1}(-1)^2... $?

Published on 26 Mar 2026 - 4:34

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Combinatorial (and Algebraic Proof) of an Identity Involving Lah Numbers

Published on 25 Mar 2026 - 9:29

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Proving a combinatorial identity: $\sum_{i=0}^m \binom{l}{i}\binom{m+n-l}{m-i} = \binom{m+n}{m}$

Published on 26 Mar 2026 - 6:06

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How evaluate sum serie with central binomial

Published on 25 Mar 2026 - 2:28

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${3^n\choose k}$ is divisible by $3$?

Published on 25 Mar 2026 - 21:01

List Question

Does this limit hold? (with mean binomial-coefficient)

Differentiation and Binomial

Problem 6.1.20 Part B From The Arts and Crafts of Problem Solving

limit of the binomial distribution

Problem 6.1.26 From The Arts and Crafts of Problem Solving

Proof of identity $\sum\limits_{k=0}^n \binom{n}{k}\binom{2k}{k}\frac{(-1)^k}{2^{2k}}=2^{-2n}\binom{2n}{n}$

Taylor expansion of $\ln(1+\sqrt{1-x})$

I want to compute this thing $\sum_{k=0}^{n}{\binom{n}{k}\frac{1}{2k+1}}$ without a dropped induction.

Combinatorial proof of $\sum_{k=0}^p {p \choose k}^2 {{n+2p-k}\choose {2p}} = {{n+p} \choose p}^2$

Sum of coefficients of even powers of x in $(1+x)^5 (1+x^2)^5$?

How is $ C_0^n+\frac{1}{2}(C_0^n-C_1^n)+\frac{1}{3}(C_0^n-C_1^n+C_2^n)+.. =C_0^{n-1}+\frac{1}{2}C_1^{n-1}(-1)+\frac{1}{3}C_2^{n-1}(-1)^2... $?

Combinatorial (and Algebraic Proof) of an Identity Involving Lah Numbers

Proving a combinatorial identity: $\sum_{i=0}^m \binom{l}{i}\binom{m+n-l}{m-i} = \binom{m+n}{m}$

How evaluate sum serie with central binomial

${3^n\choose k}$ is divisible by $3$?

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