List questions from binomial-coefficients

Published on 23 Mar 2026 - 8:20

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How to add this combinations? PLEASE HELP

Published on 25 Mar 2026 - 11:09

202

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Binomial sum of products of gamma functions

Published on 25 Mar 2026 - 10:57

141

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A Combinatorial proof for $\binom{n+1}{k}=\frac{n+1}{k}\binom{n}{k-1}$

Published on 22 Mar 2026 - 21:00

186

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Summation of binomial coefficients up to $r$ terms.

Published on 25 Mar 2026 - 12:53

182

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

Published on 23 Mar 2026 - 5:32

726

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What is the probability of getting caught?

Published on 23 Mar 2026 - 14:19

106

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Evaluate $\lim\limits_{n\rightarrow \infty} \sum\limits_{r=0}^{\infty} \frac{^n\text{C}_{r}}{n^r(r+4)}$

Published on 23 Mar 2026 - 0:00

209

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Prove that $p$ divides $(n+1)^p - n^p - 1$

Published on 25 Mar 2026 - 11:26

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Is there a formula for sum of all nCr for a given n, such that r varies from 0 to n in steps of 4.

Published on 23 Mar 2026 - 7:14

1.8k

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How to find coefficient of multiple binomial expansions quickly?

Published on 25 Mar 2026 - 15:59

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If the sum of coefficients in the expansion of (1+2x)^n is 6561 then the greatest binomial coefficient in the expansion is?

Published on 23 Mar 2026 - 14:58

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Show that if $z \in \Bbb C$ is such that $|z| < 1$, then $\sum_{n=0} ^{\infty} {a \choose n}z^n$ converges for any $a \in \Bbb C$.

Published on 22 Mar 2026 - 22:04

317

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Prove $2 \cdot \sum\limits_{k = 0}^{n} \binom{2n}{2k} = 2^{2n}$ without induction

Published on 25 Mar 2026 - 16:00

185

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How to evaluate the coefficient in this expression?

Published on 23 Mar 2026 - 10:04

List Question

Approximation Binomial theorem "Again 2"

How to add this combinations? PLEASE HELP

Binomial sum of products of gamma functions

A Combinatorial proof for $\binom{n+1}{k}=\frac{n+1}{k}\binom{n}{k-1}$

Summation of binomial coefficients up to $r$ terms.

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

What is the probability of getting caught?

Evaluate $\lim\limits_{n\rightarrow \infty} \sum\limits_{r=0}^{\infty} \frac{^n\text{C}_{r}}{n^r(r+4)}$

Prove that $p$ divides $(n+1)^p - n^p - 1$

Is there a formula for sum of all nCr for a given n, such that r varies from 0 to n in steps of 4.

How to find coefficient of multiple binomial expansions quickly?

If the sum of coefficients in the expansion of (1+2x)^n is 6561 then the greatest binomial coefficient in the expansion is?

Show that if $z \in \Bbb C$ is such that $|z| < 1$, then $\sum_{n=0} ^{\infty} {a \choose n}z^n$ converges for any $a \in \Bbb C$.

Prove $2 \cdot \sum\limits_{k = 0}^{n} \binom{2n}{2k} = 2^{2n}$ without induction

How to evaluate the coefficient in this expression?

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