Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 10G / c

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