Question

Proving $\left(\binom{n}{k}\right)=\left(\binom{n-1}{0}\right)+\left(\binom{n-1}{1}\right)+\cdots+\left(\binom{n-1}{k}\right)$

score 80 · Answer 1 · 2026-03-26 12:53:50

80

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Proving $\left(\binom{n}{k}\right)=\left(\binom{n-1}{0}\right)+\left(\binom{n-1}{1}\right)+\cdots+\left(\binom{n-1}{k}\right)$

Published on 26 Mar 2026 - 12:53

score 242 · Answer 2 · 2016-04-17 18:15:24

242

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How can I get f(x) from its Maclaurin series?

Published on 17 Apr 2016 - 18:15

score 1.9k · Answer 3 · 2016-04-18 21:05:03

1.9k

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Explanation of an Easy Proof of Variance of Bernoulli Trials

Published on 18 Apr 2016 - 21:05

score 91 · Answer 4 · 2016-04-25 03:24:52

91

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Prove that $\sum_{a_1+a_2+a_3=n}{n \choose {a_1,a_2,a_3}} = 3^n$

Published on 25 Apr 2016 - 3:24

score 36 · Answer 5 · 2016-05-03 02:05:17

36

Views

calculating $\sum_{l=0}^{\infty}\binom{l+100}{l}0.5^l 0.5^{100}$ and $\sum_{l=0}^{\infty}l \binom{l+100}{l}0.5^l 0.5^{100}$

Published on 03 May 2016 - 2:05

score 978 · Answer 6 · 2016-05-11 19:16:32

978

Views

Must the number of people...

Published on 11 May 2016 - 19:16

score 404 · Answer 7 · 2016-05-21 19:10:46

404

Views

Combinatorial proof of a certain alternating sum of binomial coefficients

Published on 21 May 2016 - 19:10

score 274 · Answer 8 · 2016-06-04 12:53:48

274

Views

Counting arguments question about sums of binomial coefficients

Published on 04 Jun 2016 - 12:53

score 245 · Answer 9 · 2016-06-20 18:52:39

245

Views

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

Published on 20 Jun 2016 - 18:52

score 139 · Answer 10 · 2016-06-20 22:26:09

139

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Combinatorial proof for a non obvious binomial identity

Published on 20 Jun 2016 - 22:26

score 1.5k · Answer 11 · 2016-06-23 15:49:48

1.5k

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Prove this using counting techniques: $\sum_{k=0}^{n}{\binom{2n+1}k} = 2^{2n}$

Published on 23 Jun 2016 - 15:49

score 550 · Answer 12 · 2013-04-03 20:13:10

550

Views

Combinatorial Proof of Binomial-type Identity

Published on 03 Apr 2013 - 20:13

score 308 · Answer 13 · 2013-04-12 18:16:34

308

Views

Finding a closed formula for $\sum_{r=0}^k {k \choose r}{k \choose r-1}$

Published on 12 Apr 2013 - 18:16

score 656 · Answer 14 · 2013-04-18 03:40:36

656

Views

Combinatorial Proof: $ n\binom {n-1}{k-1} = k \binom nk$ , where $n$ is a positive integer and $k$ is an integer.

Published on 18 Apr 2013 - 3:40

score 25.6k · Answer 15 · 2013-05-11 15:37:44

25.6k

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Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.

Published on 11 May 2013 - 15:37

List Question

Proving $\left(\binom{n}{k}\right)=\left(\binom{n-1}{0}\right)+\left(\binom{n-1}{1}\right)+\cdots+\left(\binom{n-1}{k}\right)$

How can I get f(x) from its Maclaurin series?

Explanation of an Easy Proof of Variance of Bernoulli Trials

Prove that $\sum_{a_1+a_2+a_3=n}{n \choose {a_1,a_2,a_3}} = 3^n$

calculating $\sum_{l=0}^{\infty}\binom{l+100}{l}0.5^l 0.5^{100}$ and $\sum_{l=0}^{\infty}l \binom{l+100}{l}0.5^l 0.5^{100}$

Must the number of people...

Combinatorial proof of a certain alternating sum of binomial coefficients

Counting arguments question about sums of binomial coefficients

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

Combinatorial proof for a non obvious binomial identity

Prove this using counting techniques: $\sum_{k=0}^{n}{\binom{2n+1}k} = 2^{2n}$

Combinatorial Proof of Binomial-type Identity

Finding a closed formula for $\sum_{r=0}^k {k \choose r}{k \choose r-1}$

Combinatorial Proof: $ n\binom {n-1}{k-1} = k \binom nk$ , where $n$ is a positive integer and $k$ is an integer.

Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.

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