List questions from combinatorial-proofs

Published on 03 Oct 2016 - 11:11

255

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Combinatorial Proof of $\sum_{k=1}^{n-1} k\cdot k!= n!-1 $

Published on 11 Oct 2016 - 4:18

286

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Hints on the right-hand side of a combinatorial proof question

Published on 11 Oct 2016 - 4:42

369

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Value of sum: Prove the formula using induction on n and Pascal Identity

Published on 22 Oct 2016 - 2:04

214

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Combinatorial proof of $\sum_{1\le i\le n,\ 1\le j\le n}\min(i,j)=\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

Published on 22 Oct 2016 - 11:27

342

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Prove this identity with a combinatorial argument

Published on 27 Oct 2016 - 2:29

617

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Provide a combinatorial argument to prove

Published on 27 Oct 2016 - 19:47

204

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Prove that the no. of selections of n things from two sets of n identical things and n other distinct things is (n+2)×2^(n-1)

Published on 25 Mar 2026 - 3:04

642

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Understanding the combinatorial argument for $\binom{\binom{n}{2}}{2} = 3 \binom{n+1}{4}$.

Published on 10 Nov 2016 - 15:19

154

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Combinatorial proof of the identity:

Published on 11 Nov 2016 - 0:25

876

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Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$

Published on 15 Nov 2016 - 17:21

190

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How to prove that $n \choose r$ = $\frac{n+1-r}{r}$ $n \choose r-1$ without using the factorial expansion of $n \choose r$?

Published on 18 Nov 2016 - 5:02

627

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Combinatorial proof of the identity $3^n=\sum_{k=0}^n \binom nk 2^k$

Published on 20 Nov 2016 - 1:02

61

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Please help to show the following identity

Published on 26 Nov 2016 - 9:55

73

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How do I prove this complex-looking sum-product equation?

Published on 27 Nov 2016 - 6:26

List Question

Prove $\sum \binom nk 2^k = 3^n$ this identity combinatorially

Combinatorial Proof of $\sum_{k=1}^{n-1} k\cdot k!= n!-1 $

Hints on the right-hand side of a combinatorial proof question

Value of sum: Prove the formula using induction on n and Pascal Identity

Combinatorial proof of $\sum_{1\le i\le n,\ 1\le j\le n}\min(i,j)=\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

Prove this identity with a combinatorial argument

Provide a combinatorial argument to prove

Prove that the no. of selections of n things from two sets of n identical things and n other distinct things is (n+2)×2^(n-1)

Understanding the combinatorial argument for $\binom{\binom{n}{2}}{2} = 3 \binom{n+1}{4}$.

Combinatorial proof of the identity:

Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$

How to prove that $n \choose r$ = $\frac{n+1-r}{r}$ $n \choose r-1$ without using the factorial expansion of $n \choose r$?

Combinatorial proof of the identity $3^n=\sum_{k=0}^n \binom nk 2^k$

Please help to show the following identity

How do I prove this complex-looking sum-product equation?

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