Question

Prove $\displaystyle\sum_{r=1}^{n-2} r.\binom{n-r}{2}=\binom{n+1}{4}$

score 92 · Answer 1 · 2016-03-17 19:06:32

92

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Prove $\displaystyle\sum_{r=1}^{n-2} r.\binom{n-r}{2}=\binom{n+1}{4}$

Published on 17 Mar 2016 - 19:06

score 244 · Answer 2 · 2016-03-19 18:11:41

244

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Evaluating a "binomial-like" sum

Published on 19 Mar 2016 - 18:11

score 218 · Answer 3 · 2016-03-20 19:03:04

218

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Binomial Theorem Sum

Published on 20 Mar 2016 - 19:03

score 2.4k · Answer 4 · 2016-03-20 19:29:15

2.4k

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Determine the constant term in the development of $\left(x+\frac1x\right)^6$

Published on 20 Mar 2016 - 19:29

score 404 · Answer 5 · 2016-03-20 21:19:59

If $(1+ax+bx^{2})^{10} = 1-30x+410x^{2}+...$ find the value of a and b then find the coefficient of $x^{19}$ in this expansion.

score 65 · Answer 6 · 2026-04-01 05:23:42

65

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Help with series definition, binomial theorem?

Published on 01 Apr 2026 - 5:23

score 579 · Answer 7 · 2016-03-21 17:33:31

579

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Using binomial theorem to prove an identity

Published on 21 Mar 2016 - 17:33

score 58 · Answer 8 · 2026-02-23 18:47:12

58

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Why does $\sum_{k\geq0}\binom{-r}{k}p^r(p-1)^k=p^r(1+p-1)^{-r}$?

Published on 23 Feb 2026 - 18:47

score 5.5k · Answer 9 · 2016-03-27 11:49:41

5.5k

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How is the binomial expansion of the vectors?

Published on 27 Mar 2016 - 11:49

score 47 · Answer 10 · 2016-03-27 14:56:56

47

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Binomial theroem problem

Published on 27 Mar 2016 - 14:56

score 41 · Answer 11 · 2016-03-29 13:02:13

41

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How find the value of $(a_0-a_2+a_4-\ldots)^2+(a_1-a_3+ \ldots)^2$ using $(1+x)^n=a_0+a_1x+a_2x^2+\ldots+a_nx^n$?

Published on 29 Mar 2016 - 13:02

score 42 · Answer 12 · 2016-03-30 06:41:39

42

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show equality - binomial formula, taylor?

Published on 30 Mar 2016 - 6:41

score 86 · Answer 13 · 2016-03-30 20:28:27

86

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Binomial inequality problem ${k+n-1 \choose k}\times{k+n+1 \choose k} \leq{k+n \choose k}^2$

Published on 30 Mar 2016 - 20:28

score 260 · Answer 14 · 2016-03-31 04:29:46

260

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Solving ${98 \choose 30}+2{97 \choose 30}+3 {96 \choose 30}+...+68{31 \choose 30}={100 \choose q}$ for $q$

Published on 31 Mar 2016 - 4:29

score 181 · Answer 15 · 2016-03-31 13:24:52

181

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Value of sum of binomials: $P = \binom{N}{0}-\binom{N}{1}+\binom{N}{2}-\binom{N}{3}+ \dotsb + (-1)^N\binom{N}{N}$

Published on 31 Mar 2016 - 13:24

List Question

Prove $\displaystyle\sum_{r=1}^{n-2} r.\binom{n-r}{2}=\binom{n+1}{4}$

Evaluating a "binomial-like" sum

Binomial Theorem Sum

Determine the constant term in the development of $\left(x+\frac1x\right)^6$

If $(1+ax+bx^{2})^{10} = 1-30x+410x^{2}+...$ find the value of a and b then find the coefficient of $x^{19}$ in this expansion.

Help with series definition, binomial theorem?

Using binomial theorem to prove an identity

Why does $\sum_{k\geq0}\binom{-r}{k}p^r(p-1)^k=p^r(1+p-1)^{-r}$?

How is the binomial expansion of the vectors?

Binomial theroem problem

How find the value of $(a_0-a_2+a_4-\ldots)^2+(a_1-a_3+ \ldots)^2$ using $(1+x)^n=a_0+a_1x+a_2x^2+\ldots+a_nx^n$?

show equality - binomial formula, taylor?

Binomial inequality problem ${k+n-1 \choose k}\times{k+n+1 \choose k} \leq{k+n \choose k}^2$

Solving ${98 \choose 30}+2{97 \choose 30}+3 {96 \choose 30}+...+68{31 \choose 30}={100 \choose q}$ for $q$

Value of sum of binomials: $P = \binom{N}{0}-\binom{N}{1}+\binom{N}{2}-\binom{N}{3}+ \dotsb + (-1)^N\binom{N}{N}$

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