Does anybody know a closedform solution for the following expression (N>=1)? I don't even know where to begin with the i+n denominator.
Sum of i=0 to n Combin(n,i) * (2i/(i+n)) / (2^n)
Does anybody know a closedform solution for the following expression (N>=1)? I don't even know where to begin with the i+n denominator. Sum of i=0 to n Combin(n,i) * (2i/(i+n)) / (2^n) 


$\sum_{i=0}^{n}2^{n} {n\choose i}\frac{2i}{i+n}=2^{1n}\frac{n}{1+n}F(1n,1+n;2+n;1)$ with $F$ the hypergeometric function. 

