List questions from binomial-coefficients

Published on 09 Apr 2026 - 15:23

119

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Proving $\sum_{k=0}^n \binom n k (-2)^n =(-1)^n$

Published on 25 Jul 2016 - 14:06

1.3k

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Evaluating the sums $\sum\limits_{n=1}^\infty\frac{1}{n \binom{kn}{n}}$ with $k$ a positive integer

Published on 11 Apr 2026 - 0:04

1.9k

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Prove that ${2^n-1\choose k}$ and ${2^n-k\choose k}$ ar always odd.

Published on 26 Mar 2026 - 20:44

522

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Tricky question involving binomial expansion

Published on 09 Apr 2026 - 8:10

451

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Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$

Published on 31 Mar 2026 - 3:56

70

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How to find documentation for or a proof of the following known binomial identity

Published on 10 Apr 2026 - 22:30

76

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Upper bound to a series with binomial coefficients

Published on 11 Apr 2026 - 3:32

390

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Finding binomial coefficients of product of two binomials

Published on 31 Mar 2026 - 6:08

50

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Sum of the series in terms of coefficient of $x^m$ in some binomial expansion.

Published on 27 Jul 2016 - 15:26

3.5k

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How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$

Published on 27 Mar 2026 - 15:09

145

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How can I calculate $\left[{n\atop k}\right]$?

Published on 11 Apr 2026 - 4:48

345

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Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$

Published on 02 Apr 2026 - 18:47

235

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Sum of binomial coefficients when lower suffices is same in the series: ${m \choose m}+{m+1 \choose m}+{m+2 \choose m}+...+{n \choose m}$

Published on 30 Jul 2016 - 12:13

515

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Circular permutation around 2 tables

Published on 30 Jul 2016 - 15:59

List Question

Do negative binomials imply negative factorials exist?

Proving $\sum_{k=0}^n \binom n k (-2)^n =(-1)^n$

Evaluating the sums $\sum\limits_{n=1}^\infty\frac{1}{n \binom{kn}{n}}$ with $k$ a positive integer

Prove that ${2^n-1\choose k}$ and ${2^n-k\choose k}$ ar always odd.

Tricky question involving binomial expansion

Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$

How to find documentation for or a proof of the following known binomial identity

Upper bound to a series with binomial coefficients

Finding binomial coefficients of product of two binomials

Sum of the series in terms of coefficient of $x^m$ in some binomial expansion.

How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$

How can I calculate $\left[{n\atop k}\right]$?

Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$

Sum of binomial coefficients when lower suffices is same in the series: ${m \choose m}+{m+1 \choose m}+{m+2 \choose m}+...+{n \choose m}$

Circular permutation around 2 tables

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