Let f(x)=x defined on (-p/2,p/2), extend that to a periodic definition (repeating the function over each interval of length p

the fourier series of f is

g(x)=sum( (-1)^(k+1) exp(2pi*i*k*x/p)/(2pi*i*k/p ) ,k in -infinity to infinity not equal 0)

What can we say about the convergence of g(x) to f(x)

I know g(0)=0, and I have some ideas, but no results yet. I want to know if they agree in (-p/2,p/2)