Convergence of a Taylor Series

f(x)=1/(3+2x)

Problem: For which values does the Taylor Polynomial converge to the function?

I've been working on this problem for a while messing around with Legrange's Theorem for the remainder term trying to use different bounds to show how for certain intervals of x the remainder must go to zero therefore the taylor polynomial must converge at those points. This works for some intervals but then on others it doesn't work at all. I'm wondering if I'm going about this the completely wrong way and if there's something else that I can do to show convergence? Can somebody please point me in the right direction?