Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 2 / 12F / ii / Solution

Differentiating at $s=1$ gives $\mathbb{E}{X}_{n+1}=\mu \mathbb{E}{X}_n$, hence $\mathbb{E}{X}_n={\mu }^n$.

Solved by gpt-5.6-sol high.