ZETA INFINITY?! How do you evaluate that?

The first term of the Zeta function is $1$ . For all practical purposes, for $x>>1$ , the Zeta function is just $\zeta (x)=1.$

$\displaystyle \lim_{n\to \infty}\dfrac{1}{k^n}=0$ for all $1< k\in\mathbb{N}$ . Hence $\zeta(\infty)=\fbox 1$ .