List questions from binomial-coefficients

Published on 12 Apr 2026 - 20:55

97

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Binomial theorem coefficient question

Published on 12 Apr 2026 - 14:24

143

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Lower bound on $p$ that satisfies ${p \choose n} \geq c$

Published on 31 Mar 2026 - 21:54

198

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$\gcd(m,n)$ divides $\binom{m}{n} ?$

Published on 06 Apr 2026 - 11:36

45

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Greatest Factor of $n$ that divides $\binom{n}{r}$

Published on 30 Mar 2026 - 14:25

406

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The sum $\sum_{k=0}^{3n}(-3)^k \binom{6n}{2k}=2^{6n}$

Published on 13 Apr 2026 - 2:13

63

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Given that $^_ = \frac{3}{8} \times{}^_{+1}$ and $^_ ={}^_{+6}$, find and .

Published on 12 Apr 2026 - 3:40

320

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Divisibility of $\binom{74}{37} -2$ where $\binom{74}{37}$ is a central binomial coefficient

Published on 31 Mar 2026 - 16:55

75

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$\sum_{k=0}^n\binom{n}{k}(-1)^k(k+1)$ Am I true?

Published on 03 Dec 2016 - 17:22

140

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Proving $\sum_{t=1}^j \sum_{r=1}^{t} (-1)^{r+t} \binom{j-1}{t-1} \binom{t-1}{r-1} f(r) = f(j)$

Published on 25 Mar 2026 - 12:50

100

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Solving linear recurrence with binomials

Published on 03 Apr 2026 - 7:32

816

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Combination of negative term in negative Binomial expression.

Published on 12 Apr 2026 - 2:12

98

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$\sum\limits_{n=0}^{1000000}\binom{2000000}{2n}\cdot{p}^{2n}\cdot(1-p)^{2000000-2n}$

Published on 06 Dec 2016 - 12:55

101

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Is this "combinatorial" sum equal to $1$ for every natural $m$?

Published on 11 Apr 2026 - 21:46

408

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Combinatorial identity $\sum_{k=0}^{n}\binom{n}{k}\binom{n}{k -1} = \binom{2n}{n+1}$

Published on 27 Mar 2026 - 18:26

List Question

The proof of binomial identity $\binom{j+r-1}{j}=(-1)^j \binom{-r}{j}$?

Binomial theorem coefficient question

Lower bound on $p$ that satisfies ${p \choose n} \geq c$

$\gcd(m,n)$ divides $\binom{m}{n} ?$

Greatest Factor of $n$ that divides $\binom{n}{r}$

The sum $\sum_{k=0}^{3n}(-3)^k \binom{6n}{2k}=2^{6n}$

Given that $^_ = \frac{3}{8} \times{}^_{+1}$ and $^_ ={}^_{+6}$, find and .

Divisibility of $\binom{74}{37} -2$ where $\binom{74}{37}$ is a central binomial coefficient

$\sum_{k=0}^n\binom{n}{k}(-1)^k(k+1)$ Am I true?

Proving $\sum_{t=1}^j \sum_{r=1}^{t} (-1)^{r+t} \binom{j-1}{t-1} \binom{t-1}{r-1} f(r) = f(j)$

Solving linear recurrence with binomials

Combination of negative term in negative Binomial expression.

$\sum\limits_{n=0}^{1000000}\binom{2000000}{2n}\cdot{p}^{2n}\cdot(1-p)^{2000000-2n}$

Is this "combinatorial" sum equal to $1$ for every natural $m$?

Combinatorial identity $\sum_{k=0}^{n}\binom{n}{k}\binom{n}{k -1} = \binom{2n}{n+1}$

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