My Math Forum Probability proof

 May 9th, 2017, 05:14 AM #1 Newbie   Joined: May 2017 From: Limerick Posts: 1 Thanks: 0 Probability proof Prove that Σ from r=0 to n of r(nCr)=n2^(n-1)
 May 9th, 2017, 06:36 PM #2 Senior Member     Joined: Sep 2015 From: CA Posts: 1,237 Thanks: 637 start with $(1+x)^n = \sum \limits_{k=0}^n~\dbinom{n}{k}x^k$ differentiate both sides and let $x=1$
 May 9th, 2017, 06:37 PM #3 Global Moderator   Joined: May 2007 Posts: 6,234 Thanks: 496 r(nCr)=n([n-1]C[r-1]) Sum over r gives result.

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