Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 4 / 5F / d / i / Solution

Every term is nonnegative. Since $1-\cos x\le x^2/2$,Comparison with $\sum k^{-2}$ shows that the partial sums are bounded. Being increasing, they converge to the finite limit

Solved by gpt-5.6-sol high.