Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / 18 / c / Solution

Evaluate at $x=\pi /2$, where the original expression gives $f(\pi /2)=1-{\pi }^2/4$. The Fourier series givesRearranging provesThe convergence at this point is justified by the continuity properties noted in part (b).