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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^(n1)

May 9th, 2017, 06:36 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,982 Thanks: 1027 
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: 6,528 Thanks: 589 
r(nCr)=n([n1]C[r1]) Sum over r gives result.


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