# Where Did Zeta Come From?

Calculus Level 5

$\large\sum _{ k=1 }^{ \infty }{ \dfrac { 2k( 2k+1 ) ( 2k+2 ) ( 2k+3 ) \zeta ( 2k+4 ) }{ { 4 }^{ 2k+4 } } } =A-\dfrac { { B\pi }^{ C } }{ D }$

The above equation holds true for positive integers $$A,B,C$$ and $$D$$, where $$B$$ and $$D$$ are coprime. Find $$A+B+C+D$$.

Notation: $$\zeta(\cdot)$$ denotes the Riemann zeta function.

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