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September 20th, 2016, 02:11 AM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  Binomial Series Sum
Sum of series $\displaystyle \displaystyle \sum_{0\leq i<j\leq n}j\binom{n}{i}$

September 20th, 2016, 02:51 AM  #2 
Senior Member Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 
here is a starting point write your sum S as S=$\sum_{i=0}^{n1}\sum_{j=i+1}^{n}j\binom{n}{i}$ $=\sum_{i=0}^{n1}\binom{n}{i}\sum_{j=i+1}^nj$ and use $1+2+3+....K=\frac{K(K+1)}{2}$ 

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binomial, series, sum 
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