List questions from binomial-coefficients

Published on 08 Apr 2026 - 21:04

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Combinatorial proof of an identity on sum of elements in a grid

Published on 10 Oct 2016 - 8:56

2.4k

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How to prove the sum of triangular numbers in the form n(n+1)(n+2)/6?

Published on 10 Oct 2016 - 9:06

249

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Find $n$ in this binomial expansion.

Published on 31 Mar 2026 - 10:45

164

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Prove $a {a+b \choose b}$ divides the lowest common multiple of $b+1, b+2, ..., b+a$

Published on 06 Apr 2026 - 1:09

102

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Showing $\Bigg[\sum_{n=0}^{\infty}\frac{{2n}\choose{n}}{4^n}x^n\Bigg]^2=\sum_{n=0}^{\infty}x^n$

Published on 12 Oct 2016 - 2:44

75

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Solving $\binom{39}{5+2x}=\binom{39}{2x-2}$

Published on 12 Oct 2016 - 13:18

1.1k

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Determine infinite sum with shifting binomial coefficients

Published on 11 Apr 2026 - 20:08

510

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summation of Newton symbol product

Published on 12 Apr 2026 - 1:22

1.6k

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Limit $\lim_{n\to\infty}\sum_{k=0}^n\binom nk\frac{3k}{2^n(n+3k)}$

Published on 14 Oct 2016 - 8:15

68

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Another Binomial

Published on 11 Apr 2026 - 7:27

325

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Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$

Published on 14 Oct 2016 - 22:43

91

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Solve for y $\frac{y!}{(y-2)!2!}+10y=108$

Published on 04 Apr 2026 - 19:14

183

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Finding $\lim_{n\rightarrow \infty} \sqrt[n]{\binom{\alpha n}{n}}$

Published on 15 Oct 2016 - 10:21

696

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Evaluate $\sum^{n-1}_{k=1} {n\choose k}\frac{kn^{n-k}}{k+1}$

Published on 15 Oct 2016 - 15:00

List Question

Find a closed formula to the sum: $\sum_{k=2}^{50}k (k-1){50 \choose k}$

Combinatorial proof of an identity on sum of elements in a grid

How to prove the sum of triangular numbers in the form n(n+1)(n+2)/6?

Find $n$ in this binomial expansion.

Prove $a {a+b \choose b}$ divides the lowest common multiple of $b+1, b+2, ..., b+a$

Showing $\Bigg[\sum_{n=0}^{\infty}\frac{{2n}\choose{n}}{4^n}x^n\Bigg]^2=\sum_{n=0}^{\infty}x^n$

Solving $\binom{39}{5+2x}=\binom{39}{2x-2}$

Determine infinite sum with shifting binomial coefficients

summation of Newton symbol product

Limit $\lim_{n\to\infty}\sum_{k=0}^n\binom nk\frac{3k}{2^n(n+3k)}$

Another Binomial

Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$

Solve for y $\frac{y!}{(y-2)!2!}+10y=108$

Finding $\lim_{n\rightarrow \infty} \sqrt[n]{\binom{\alpha n}{n}}$

Evaluate $\sum^{n-1}_{k=1} {n\choose k}\frac{kn^{n-k}}{k+1}$

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