Question

Expected number of passengers for the flight

score 1.6k · Answer 1 · 2026-03-26 07:33:25

Expected number of passengers for the flight

Published on 26 Mar 2026 - 7:33

score 458 · Answer 2 · 2014-11-12 21:37:27

Binomial identity $\binom{0}{0}\binom{2n}{n}+\binom{2}{1}\binom{2n-2}{n-1}+\binom{4}{2}\binom{2n-4}{n-2}+\cdots+\binom{2n}{n}\binom{0}{0}=4^n.$

score 689 · Answer 3 · 2014-11-13 21:38:18

689

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Evaluating $\sum_{n=i}^{\infty} {2n \choose n-i}^{-1}$

Published on 13 Nov 2014 - 21:38

score 229 · Answer 4 · 2026-04-02 22:27:35

229

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What is the coefficient of $x^{25}$ in $(x^3 + x + 1)^{10}$?

Published on 02 Apr 2026 - 22:27

score 134 · Answer 5 · 2026-04-05 08:50:53

134

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n-th Derivative

Published on 05 Apr 2026 - 8:50

score 75 · Answer 6 · 2026-03-29 04:44:07

75

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Silly mistake on evaluating the sixth term of $\left (\frac{a}{b}+\frac{b}{a^2}\right)^{17}$?

Published on 29 Mar 2026 - 4:44

score 443 · Answer 7 · 2014-11-17 00:10:07

443

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Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$

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score 3.2k · Answer 8 · 2026-03-30 12:47:59

3.2k

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Counting binary strings that have atmost k consecutive 0's

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score 72 · Answer 9 · 2014-11-17 16:53:54

72

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If $C_0,C_1,C_2,\cdots C_n$ denotes the binomial coefficients in the expansion of $(1+x)^n$ then $\sum^n_{r=0}\sum^n_{s=0} (C_r+C_s)$ =?

Published on 17 Nov 2014 - 16:53

score 129 · Answer 10 · 2026-03-28 21:44:22

129

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Compute $\sum\limits_{k=0}^n (-1)^k \binom{n}{k}\frac{1}{s+k}$

Published on 28 Mar 2026 - 21:44

score 2.5k · Answer 11 · 2026-03-25 11:08:08

2.5k

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Combinatorial proof (multi choose)

Published on 25 Mar 2026 - 11:08

score 33 · Answer 12 · 2014-11-19 14:57:00

33

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Evaluation of $\sum\limits_{i = 0}^s {\left( {\begin{array}{*{20}{c}} q \\ {{2^i}} \end{array}} \right)}$

Published on 19 Nov 2014 - 14:57

score 158 · Answer 13 · 2014-11-20 04:59:06

158

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Proving binomial coefficients identity: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$

Published on 20 Nov 2014 - 4:59

score 91 · Answer 14 · 2014-11-20 14:29:07

91

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Definition of binomial coefficient

Published on 20 Nov 2014 - 14:29

score 177 · Answer 15 · 2014-11-20 23:53:07

177

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Sum function operation: coefficient.

Published on 20 Nov 2014 - 23:53

List Question

Expected number of passengers for the flight

Binomial identity $\binom{0}{0}\binom{2n}{n}+\binom{2}{1}\binom{2n-2}{n-1}+\binom{4}{2}\binom{2n-4}{n-2}+\cdots+\binom{2n}{n}\binom{0}{0}=4^n.$

Evaluating $\sum_{n=i}^{\infty} {2n \choose n-i}^{-1}$

What is the coefficient of $x^{25}$ in $(x^3 + x + 1)^{10}$?

n-th Derivative

Silly mistake on evaluating the sixth term of $\left (\frac{a}{b}+\frac{b}{a^2}\right)^{17}$?

Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$

Counting binary strings that have atmost k consecutive 0's

If $C_0,C_1,C_2,\cdots C_n$ denotes the binomial coefficients in the expansion of $(1+x)^n$ then $\sum^n_{r=0}\sum^n_{s=0} (C_r+C_s)$ =?

Compute $\sum\limits_{k=0}^n (-1)^k \binom{n}{k}\frac{1}{s+k}$

Combinatorial proof (multi choose)

Evaluation of $\sum\limits_{i = 0}^s {\left( {\begin{array}{*{20}{c}} q \\ {{2^i}} \end{array}} \right)}$

Proving binomial coefficients identity: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$

Definition of binomial coefficient

Sum function operation: coefficient.

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