Actually obtaining the series shouldn't be that bad. For
And you'll get something very similar for
Can you take it from here?
first the function must be periodic to be developed in Fourier series.
I consider that the function has a period of 2pi look the attachement. And it's clear that the function is even thus the (bn) coefficients are null.
and about the convergence: The serie converge to f(x) where f(x) is continous
and diverge where f(x) is discontinous
this is from the lejeune-dirichlet theorem: