List questions from binomial-coefficients

Published on 31 Mar 2020 - 11:55

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The Polynomials $P_n(x+y)$

Published on 01 Apr 2020 - 8:16

158

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Proving that $n!$ divides $a(a+1)(a+2)...(a+n-1)$

Published on 01 Apr 2020 - 9:52

36

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Summation of binomial coefficients with indices having difference of 4

Published on 01 Apr 2020 - 11:05

58

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Evaluate:$\sum_{s=0}^{N}(-1)^s{2s \choose s}{N+s \choose N-s}\frac{s^2}{(s+1)^2}$

Published on 01 Apr 2020 - 12:00

31

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Get n terms from binomial coefficient

Published on 01 Apr 2020 - 18:05

25

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How can i represent the terms of the following sequence?

Published on 01 Apr 2020 - 19:22

97

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calculating allowable paths

Published on 25 Mar 2026 - 20:51

54

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how can I prove with induction this: $\binom{2n}{0}\le \binom{2n}{1}\le\binom{2n}{2}\le \cdots\le \binom{2n}{n}$?

Published on 01 Apr 2020 - 22:43

142

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Double sum of a triple-product of binomial coefficients geometric series

Published on 25 Mar 2026 - 15:53

58

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How to find the number of integers of the form $\overline{a_7a_6a_5...a_1}$ where $\forall i,$ $a_i\leq a_{i+1}$ and $a_7 \neq 0$

Published on 07 Apr 2026 - 19:35

402

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Function defining $nCr$

Published on 02 Apr 2020 - 8:13

91

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calculating total number of allowable paths

Published on 25 Mar 2026 - 20:52

412

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$\sum_{j:0\leq n+jk\leq N}\binom{N}{n+jk}p^{n+jk}(1-p)^{N-n-jk}\to 1/k$ as $N\to\infty$ for any given $k\in\mathbb N$ and $n=0,1,\cdots,k-1$?

Published on 03 Apr 2020 - 13:01

77

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What is the greatest term in $(1+\frac{1}{2}x)^{12}$ when $x=\frac{1}{2}\;?$

Published on 30 Mar 2026 - 6:12

List Question

Simplify a series involving binomial coefficients

The Polynomials $P_n(x+y)$

Proving that $n!$ divides $a(a+1)(a+2)...(a+n-1)$

Summation of binomial coefficients with indices having difference of 4

Evaluate:$\sum_{s=0}^{N}(-1)^s{2s \choose s}{N+s \choose N-s}\frac{s^2}{(s+1)^2}$

Get n terms from binomial coefficient

How can i represent the terms of the following sequence?

calculating allowable paths

how can I prove with induction this: $\binom{2n}{0}\le \binom{2n}{1}\le\binom{2n}{2}\le \cdots\le \binom{2n}{n}$?

Double sum of a triple-product of binomial coefficients geometric series

How to find the number of integers of the form $\overline{a_7a_6a_5...a_1}$ where $\forall i,$ $a_i\leq a_{i+1}$ and $a_7 \neq 0$

Function defining $nCr$

calculating total number of allowable paths

$\sum_{j:0\leq n+jk\leq N}\binom{N}{n+jk}p^{n+jk}(1-p)^{N-n-jk}\to 1/k$ as $N\to\infty$ for any given $k\in\mathbb N$ and $n=0,1,\cdots,k-1$?

What is the greatest term in $(1+\frac{1}{2}x)^{12}$ when $x=\frac{1}{2}\;?$

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