Solution
= Solution
For each $a\gt 1$, $n^{-x}\le n^{-a}$ on $[a,\infty)$ and the p-series converges. The M-test gives locally <uniform convergence> there, so the sum $\zeta$ is continuous on $(1,\infty)$.
= Solution
For each $a\gt 1$, $n^{-x}\le n^{-a}$ on $[a,\infty)$ and the p-series converges. The M-test gives locally <uniform convergence> there, so the sum $\zeta$ is continuous on $(1,\infty)$.