Let $$\zeta(x)$$ be the Zeta function (where, for convenience, $$x$$ is assumed to be $$> 1$$).
$$\zeta(x) = \sum_{k=1}^{\infty}\frac{1}{k^x}$$Similarly, define the Eta function (alternating Zeta function) by the following series - where again, in this case, we assume $$x > 1$$:$$\eta(x) =...