A question says, show that $\sum_{n=1}^\infty n^{-x} $ converges pointwise but not uniformly for $x \in (1,\infty)$. I can show it converges pointwise by taking $x\in (1+\delta, \infty)$ for any $x$ and $\delta>0$ and then using the Weierstrass-M test on $1+\delta$.
But I'm struggeling to show that it doesn't converge uniformly? Thanks!