Question

Finding the exponent $n$ in a binomial expansion given that the coefficient of $x^3$ is 4 times greater than the coefficient of $x^2$

score 1.9k · Answer 1 · 2026-03-29 21:14:48

1.9k

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Finding the exponent $n$ in a binomial expansion given that the coefficient of $x^3$ is 4 times greater than the coefficient of $x^2$

Published on 29 Mar 2026 - 21:14

score 96 · Answer 2 · 2026-03-29 20:02:09

96

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Scaling of a sum with factorials

Published on 29 Mar 2026 - 20:02

score 71 · Answer 3 · 2020-02-10 21:17:49

71

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Number of combinations of $m$ ordered sets

Published on 10 Feb 2020 - 21:17

score 90 · Answer 4 · 2020-02-11 18:47:23

90

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Pine tree shaped in binomial coefficients and a proving the formula derived from the shape

Published on 11 Feb 2020 - 18:47

score 48 · Answer 5 · 2020-02-12 22:46:15

48

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Sum of multiplication of binomial with consecutive rising term

Published on 12 Feb 2020 - 22:46

score 341 · Answer 6 · 2026-03-29 21:14:48

341

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prove $ \sum_{m=0}^{n-k} {n-m-1\choose n-k-m} \\ = [z^{n-k}] (1+z)^{n-1} \sum_{m=0}^{n-k} z^m (1+z)^{-m} $

Published on 29 Mar 2026 - 21:14

score 106 · Answer 7 · 2026-03-27 06:13:26

106

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How to compute $H_{5+\sqrt{7}}$

Published on 27 Mar 2026 - 6:13

score 518 · Answer 8 · 2026-03-27 00:56:25

518

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A Vandermonde Identity for Stirling Numbers?

Published on 27 Mar 2026 - 0:56

score 149 · Answer 9 · 2026-03-29 21:40:30

149

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Can you prove/disprove $\int_{-\infty}^{\infty}{\frac{x!}{(x-t)!(t)!}dt} = 2^x$

Published on 29 Mar 2026 - 21:40

score 151 · Answer 10 · 2026-03-25 20:52:48

151

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calculating total number of allowable paths from $(0,0)$ to $(5,5)$

Published on 25 Mar 2026 - 20:52

score 98 · Answer 11 · 2020-02-14 21:16:12

98

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Show that ${n+k-1 \choose k}={n+k-2\choose k}+{n+k-1 \choose k-1}$

Published on 14 Feb 2020 - 21:16

score 58 · Answer 12 · 2020-02-15 14:08:01

58

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prove $\frac{1}{x^n+1}=\prod_{k=1}^n(x-x_k)^{-1}$

Published on 15 Feb 2020 - 14:08

score 233 · Answer 13 · 2026-03-27 08:57:31

233

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Counting Solutions to $x_1 + x_2 + \dots + x_k = n$ with $x_i \leq r$ Closed Form

Published on 27 Mar 2026 - 8:57

score 58 · Answer 14 · 2020-02-16 19:05:50

58

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Show that $\dbinom{2n}{n} + \dbinom{2n}{n-1} = \frac{1}{2} \dbinom{2n+2}{n+1}$

Published on 16 Feb 2020 - 19:05

score 140 · Answer 15 · 2020-02-16 19:10:46

140

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$m=\sum_{k=1}^{2017}k^3\binom{n}{k}$. Find m.

Published on 16 Feb 2020 - 19:10

List Question

Finding the exponent $n$ in a binomial expansion given that the coefficient of $x^3$ is 4 times greater than the coefficient of $x^2$

Scaling of a sum with factorials

Number of combinations of $m$ ordered sets

Pine tree shaped in binomial coefficients and a proving the formula derived from the shape

Sum of multiplication of binomial with consecutive rising term

prove $ \sum_{m=0}^{n-k} {n-m-1\choose n-k-m} \\ = [z^{n-k}] (1+z)^{n-1} \sum_{m=0}^{n-k} z^m (1+z)^{-m} $

How to compute $H_{5+\sqrt{7}}$

A Vandermonde Identity for Stirling Numbers?

Can you prove/disprove $\int_{-\infty}^{\infty}{\frac{x!}{(x-t)!(t)!}dt} = 2^x$

calculating total number of allowable paths from $(0,0)$ to $(5,5)$

Show that ${n+k-1 \choose k}={n+k-2\choose k}+{n+k-1 \choose k-1}$

prove $\frac{1}{x^n+1}=\prod_{k=1}^n(x-x_k)^{-1}$

Counting Solutions to $x_1 + x_2 + \dots + x_k = n$ with $x_i \leq r$ Closed Form

Show that $\dbinom{2n}{n} + \dbinom{2n}{n-1} = \frac{1}{2} \dbinom{2n+2}{n+1}$

$m=\sum_{k=1}^{2017}k^3\binom{n}{k}$. Find m.

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