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September 20th, 2016, 02:11 AM   #1
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Binomial Series Sum

Sum of series $\displaystyle \displaystyle \sum_{0\leq i<j\leq n}j\binom{n}{i}$
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September 20th, 2016, 02:51 AM   #2
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here is a starting point


write your sum S as

S=$\sum_{i=0}^{n-1}\sum_{j=i+1}^{n}j\binom{n}{i}$

$=\sum_{i=0}^{n-1}\binom{n}{i}\sum_{j=i+1}^nj$

and use $1+2+3+....K=\frac{K(K+1)}{2}$
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