List questions from binomial-coefficients

Published on 13 Apr 2026 - 6:05

143

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Can one expand $(a + b)^{{i}}$?

Published on 11 Apr 2026 - 23:24

571

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primes and binomial coefficients

Published on 15 Apr 2026 - 13:31

114

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Prove that $\sum_{k=0}^{n}\binom{n}{k}\frac{1}{2n-2k+1}=\frac{(2n)!!}{(2n+1)!!}$

Published on 15 Apr 2026 - 13:50

100

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Sum of products of binomial coefficients.

Published on 13 Apr 2026 - 22:08

117

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Expectation of the max number of times an element is chosen, if repeatedly randomly choosing a subset out of a set

Published on 14 Apr 2026 - 18:44

40

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How to prove $\sum_{k=0}^{n-1}(-1)^k\binom{n+k}{2k+1}C_k=1$?

Published on 25 Mar 2026 - 23:11

129

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Evaluating $\binom{40}{0}\binom{20}{10}+\binom{41}{1}\binom{19}{10}+\cdots+\binom{50}{10}\binom{10}{10}$

Published on 16 Apr 2026 - 2:18

141

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How do you prove that $\sum\limits_{r=0}^{n}\binom{n}{r}\binom{n+r}{r} =\sum\limits_{r=0}^{n}( -1)^{n-r} 2^{r}\binom{n}{r}\binom{n+r}{r}$?

Published on 14 Apr 2026 - 23:46

78

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Find the value of $A,$ a summation

Published on 12 Apr 2026 - 20:10

164

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Prove that $\sum_{k=1}^n\frac{\prod_{1\leq r\leq n, r\neq m}(x+k-r)}{\prod_{1\leq r\leq n, r\neq k}(k-r)}=1$

Published on 16 Apr 2026 - 9:08

139

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Finding $\arg\min \sum_{j=1}^n \binom{n}{j} \frac{1}{1-(1-2x)^j}$ for $x \in (0, 1)$.

Published on 16 Apr 2026 - 16:28

41

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Correlation of a binomial RV with itself

Published on 09 Apr 2026 - 13:25

91

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A summation formula for number of ways $n$ identical objects can be put in $m$ identical bins

Published on 14 Apr 2026 - 9:15

160

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Showing the root of $\sum_{j=1}^n \binom{n}{j} \frac{j x^{j-1}}{(1-x^j)^2}$ approaches $0$ as $n \to \infty$.

Published on 20 Apr 2026 - 10:06

List Question

Sum of binomial coefficient equation

Can one expand $(a + b)^{{i}}$?

primes and binomial coefficients

Prove that $\sum_{k=0}^{n}\binom{n}{k}\frac{1}{2n-2k+1}=\frac{(2n)!!}{(2n+1)!!}$

Sum of products of binomial coefficients.

Expectation of the max number of times an element is chosen, if repeatedly randomly choosing a subset out of a set

How to prove $\sum_{k=0}^{n-1}(-1)^k\binom{n+k}{2k+1}C_k=1$?

Evaluating $\binom{40}{0}\binom{20}{10}+\binom{41}{1}\binom{19}{10}+\cdots+\binom{50}{10}\binom{10}{10}$

How do you prove that $\sum\limits_{r=0}^{n}\binom{n}{r}\binom{n+r}{r} =\sum\limits_{r=0}^{n}( -1)^{n-r} 2^{r}\binom{n}{r}\binom{n+r}{r}$?

Find the value of $A,$ a summation

Prove that $\sum_{k=1}^n\frac{\prod_{1\leq r\leq n, r\neq m}(x+k-r)}{\prod_{1\leq r\leq n, r\neq k}(k-r)}=1$

Finding $\arg\min \sum_{j=1}^n \binom{n}{j} \frac{1}{1-(1-2x)^j}$ for $x \in (0, 1)$.

Correlation of a binomial RV with itself

A summation formula for number of ways $n$ identical objects can be put in $m$ identical bins

Showing the root of $\sum_{j=1}^n \binom{n}{j} \frac{j x^{j-1}}{(1-x^j)^2}$ approaches $0$ as $n \to \infty$.

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