# Interesting Zeta

Calculus Level pending

$\large \displaystyle \sum_{k=2}^{\infty} \frac{\zeta(k)-1}{k+1} = \frac{A}{B} - \frac{C}{B}\ln(D \pi) - \frac{\gamma}{B}$

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

Notation: $$\gamma \approx 0.5772$$ denotes the Euler-Mascheroni constant.

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