Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Does anybody know a closed-form 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)

share|improve this question

1 Answer 1

up vote 1 down vote accepted

$\sum_{i=0}^{n}2^{-n} {n\choose i}\frac{2i}{i+n}=2^{1-n}\frac{n}{1+n}F(1-n,1+n;2+n;-1)$

with $F$ the hypergeometric function.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.