List questions from binomial-coefficients

Published on 23 Mar 2026 - 2:03

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General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.

Published on 23 Mar 2026 - 2:37

86

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The proof Pascal's triangle

Published on 22 Mar 2026 - 22:17

118

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Sum of $\sum_{0\leq k\leq n}k\binom{n}{k}p^k(1-p)^{n-k}$

Published on 23 Mar 2026 - 4:57

141

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Is $(ab+1)^{a^n}-1$ always divisible by $a^{n+1}b$?

Published on 25 Mar 2026 - 13:04

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There are 4 red, 3 green and 6 white balls in a jar. In how many ways is it possible to choose 6 balls if there must be one of each color?

Published on 22 Mar 2026 - 23:37

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Closed form of $\sum_{k=0}^n\binom{2k}{k}(-1/4)^k$

Published on 25 Mar 2026 - 5:02

520

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Prove that ${F_{n+1}} = \sum_{k=0}^{n}\binom{n-k}{k}$ where ${F_{n}}$ is n-th Fibonacci number

Published on 25 Mar 2026 - 6:06

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Closed form for a combinatorial series - Convolution.

Published on 25 Mar 2026 - 6:31

176

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Prove that $\sum_{k=1}^n\binom{2n-1}{n-k}=4^{n-1}$.

Published on 23 Mar 2026 - 1:22

492

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Prove an alternating binomial sum with odd weights

Published on 22 Mar 2026 - 22:10

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Upper bound for $\sum\limits_{k=1}^{n} \binom{n}{k} 2^{2^k}$

Published on 22 Mar 2026 - 20:51

127

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How was the following lower bound on ${n \choose pn}$ derived?

Published on 25 Mar 2026 - 14:23

109

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simplify $\log(x^k(1-x)^{n-k}) - \log(x^k(1-x)^{n-k} + (1-x)^k x^{n-k}) - \log(0.5))$ for $x \in (0,1)$

Published on 22 Mar 2026 - 21:05

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How the sum $\sum_{j=0}^m {n \choose j}{2n+m-j-1\choose m-j}(-2)^j$ scales with $n$

Published on 23 Mar 2026 - 8:54

List Question

Binomial Coefficients $ {\frac{-1}{2} \choose n}$

General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.

The proof Pascal's triangle

Sum of $\sum_{0\leq k\leq n}k\binom{n}{k}p^k(1-p)^{n-k}$

Is $(ab+1)^{a^n}-1$ always divisible by $a^{n+1}b$?

There are 4 red, 3 green and 6 white balls in a jar. In how many ways is it possible to choose 6 balls if there must be one of each color?

Closed form of $\sum_{k=0}^n\binom{2k}{k}(-1/4)^k$

Prove that ${F_{n+1}} = \sum_{k=0}^{n}\binom{n-k}{k}$ where ${F_{n}}$ is n-th Fibonacci number

Closed form for a combinatorial series - Convolution.

Prove that $\sum_{k=1}^n\binom{2n-1}{n-k}=4^{n-1}$.

Prove an alternating binomial sum with odd weights

Upper bound for $\sum\limits_{k=1}^{n} \binom{n}{k} 2^{2^k}$

How was the following lower bound on ${n \choose pn}$ derived?

simplify $\log(x^k(1-x)^{n-k}) - \log(x^k(1-x)^{n-k} + (1-x)^k x^{n-k}) - \log(0.5))$ for $x \in (0,1)$

How the sum $\sum_{j=0}^m {n \choose j}{2n+m-j-1\choose m-j}(-2)^j$ scales with $n$

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