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May 9th, 2017, 05:14 AM   #1
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Probability proof

Prove that Σ from r=0 to n of r(nCr)=n2^(n-1)
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May 9th, 2017, 06:36 PM   #2
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start with

$(1+x)^n = \sum \limits_{k=0}^n~\dbinom{n}{k}x^k$

differentiate both sides and let $x=1$
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May 9th, 2017, 06:37 PM   #3
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r(nCr)=n([n-1]C[r-1]) Sum over r gives result.
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