Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 224 / 3 / a / Solution

For nonnegative numbers $a_i,b_i$, put $a={\sum }_i{a}_i$ and $b={\sum }_i{b}_i$. The log-sum inequality iswith $0\log (0/b)=0$ and the usual extended-value convention when a denominator vanishes. Equality holds precisely when $a_i/b_i$ is constant over the indices with $a_i>0$.

Solved by gpt-5.6-sol high.