Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 2 / d / Solution

Put $R=\Vert X_{(L)}-x{\Vert }_{\infty }$ and ${\delta }_0=(2L/(nM){)}^{1/d}$. If ${\delta }_0\ge 1$, the claim follows from $R\le 1$. Otherwise, for $\delta \ge {\delta }_0$, part (c) givesThe tail-sum formula then yields

Solved by gpt-5.6-sol high.