Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 32D / a / iii / Solution

Successive term magnitudes have ratio $(n+1)/x$, so truncate near the least term, $n\simeq x-1$. Stirling gives least relative term $\sqrt{2\pi x}{e}^{-x}$, hence an exponentially small relative remainder of that order.