List questions from binomial-coefficients

Published on 15 Apr 2026 - 0:21

101

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Show that $\binom{1/2}{k} = \frac{(-1)^{k+1}}{4^k(2k-1)}\binom{2k}{k}$

Published on 14 Apr 2026 - 12:36

83

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How to compute the summation of a binomial coefficient/ show the following is true

Published on 13 Apr 2026 - 1:45

2.9k

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How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?

Published on 16 Apr 2026 - 8:06

43

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Integer Series Expansion

Published on 10 Apr 2026 - 6:35

419

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Remove first element of sequence, compute cumulative sum, iterate

Published on 14 Apr 2026 - 10:12

104

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Show $\sum_{n=0}^{\infty}\binom{n+k}{k}z^{n}=\frac{1}{(1-z)^{k+1}}$

Published on 13 Apr 2026 - 17:47

8k

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Asymptotic for binomial coefficients

Published on 14 Apr 2026 - 15:19

1.1k

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Number of ways to combine two sets of values

Published on 16 Apr 2026 - 11:38

14.4k

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Intuitive explanation of binomial coefficient

Published on 12 Apr 2026 - 6:55

226

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Trailing zeroes in binomial coefficient

Published on 12 Apr 2026 - 20:59

728

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How is the Binomial coefficient simplified to a falling factorial?

Published on 12 Apr 2026 - 18:23

2.1k

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Find the number of solutions of the equation $x+y +z +w = 15$ in the following cases:

Published on 15 Apr 2026 - 20:22

303

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Dealing with floor function in binomial coefficients

Published on 09 Apr 2026 - 2:02

43

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How to show $u_n=\binom{n}{l}\Rightarrow s_n=\binom{n+1}{l+1}$?

Published on 14 Apr 2026 - 11:42

List Question

How to show C(n,k)= C(n,n-k)

Show that $\binom{1/2}{k} = \frac{(-1)^{k+1}}{4^k(2k-1)}\binom{2k}{k}$

How to compute the summation of a binomial coefficient/ show the following is true

How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?

Integer Series Expansion

Remove first element of sequence, compute cumulative sum, iterate

Show $\sum_{n=0}^{\infty}\binom{n+k}{k}z^{n}=\frac{1}{(1-z)^{k+1}}$

Asymptotic for binomial coefficients

Number of ways to combine two sets of values

Intuitive explanation of binomial coefficient

Trailing zeroes in binomial coefficient

How is the Binomial coefficient simplified to a falling factorial?

Find the number of solutions of the equation $x+y +z +w = 15$ in the following cases:

Dealing with floor function in binomial coefficients

How to show $u_n=\binom{n}{l}\Rightarrow s_n=\binom{n+1}{l+1}$?

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