Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics V resit / Question 4 / c / Solution

Set $p=3$ and $x=0$ in the Fourier series from b. Since the function is continuous there, pointwise convergence of a piecewise smooth Fourier series givesIt follows thatThe $n=1$ and $n=2$ terms are $1/8$ and $-1/5$, respectively. Subtracting them gives the required absolutely convergent series: