Convergence of the Real analysis

Question

The question is find the Fourier series of "|cost| for all t". I already found the fourier series

But now the question asks " At which values of $x$, does the series fail to converge to ? To what values does it converge at those points? "

So what to do ?

Answer 1

That will converge for all $x$; the function is Lipschitz continuous, and so its Fourier series converges everywhere. (see, for instance, the answer to this question)