Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 1 / 3F / b / Solution

For every $N$, the Cauchy-Schwarz inequality givesThe right-hand side is bounded independently of $N$. Since the summands are positive, the partial sums increase to a finite limit, proving the geometric means of two summable positive sequences result.

Solved by gpt-5.6-sol high.