# Who's up to the challenge?18

Calculus Level 5

$\large \displaystyle\sum _{ k=1 }^{ \infty }{ \displaystyle\sum _{ n={ 2 }^{ k-1 }+1 }^{ { 2 }^{ k } }{ \frac { k }{ 2n(2n-1) } } }$

If the value of the series above is equal to $$A-B\gamma$$, where $$A$$ and $$B$$ are positive integers, find $$A+B$$.

Notation: $$\gamma$$ denotes the Euler-Mascheroni constant.

this is a part of Who's up to the challenge?

×