# Summing the zeta function

Calculus Level 5

Suppose $$a_k=\zeta (2k),$$ where $$\zeta$$ is the Riemann zeta function. What is the value of the sum $$\sum \limits_{k=1}^{\infty }\frac{\zeta(2k)-1}{k}$$?

Details and assumptions

The Riemann zeta function $$\zeta(s)$$ is defined as $$\sum \limits_{n=1}^{\infty} n^{-s}.$$

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