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panky September 20th, 2016 02:11 AM

Binomial Series Sum
 
Sum of series $\displaystyle \displaystyle \sum_{0\leq i<j\leq n}j\binom{n}{i}$

abdallahhammam September 20th, 2016 02:51 AM

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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