Summing the zeta function

Calculus Level 5

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

Details and assumptions

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

×

Problem Loading...

Note Loading...

Set Loading...