Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 6 / a / iv / Solution

At $x=1$, the left limit is $1$. The right limit is $-1$ because of the period-two extension. Therefore Dirichlet's theorem on Fourier series gives the Fourier series limitEvery Fourier partial sum is also exactly zero there because $\sin ((2j+1)\pi )=0$.