# Who's up to the challenge? 58

Calculus Level 5

$\large \sum_{n=1}^\infty \dfrac{ \zeta(2n)}{(n+1) 2^{4n}} = \dfrac AB - \dfrac {CK}\pi - \dfrac 1D \ln F + \dfrac G{H\pi^I} \zeta(J)$

The equation above holds true for positive integers $$A,B,C,D,F,G,H,I$$ and $$J$$ such that $$\gcd(A,B) = \gcd(G,H) = 1$$ and $$F$$ is minimized.

Find $$A+B+C+D+F+G+H+I+J$$.

Notations:

×