# Who's up to the challenge? 42

Calculus Level 5

$\large \sum_{n=1}^\infty (-1)^n \left( \ln 2 - \dfrac1{n+1} - \dfrac1{n+2} - \cdots - \dfrac1{n+n} \right)^2$

The value of the series above is equal to

$\large \dfrac Ga + \dfrac{\pi^b } c - \dfrac \pi d \ln f - \dfrac gh (\ln j)^i \; ,$

where $$a,b,c,d,f,g,h,i$$ and $$j$$ are positive integers with $$\gcd(g,h) = 1$$ and $$G$$ denotes the Catalan's constant.

Find $$a+b+c+d+f+g+h+i+j$$.

×