Let denote the Riemann zeta function. Evaluate the series

*(Seraphim Tsipelis, Anastasios Kotronis)*

**Solution**

To what follows stands for

Then it is known that . Integrating we get that

(1)

Setting back at and substracting these two equations we get that

(2)

Integrating both sides of we get that

and thus

A very similar result is the following: