Uniform convergence on a closed interval - power series Basically, I want to prove that a power serie is uniformly convergent on [-1,1].  I have calculated that it's radius of convergence R is equal to 1, implying that the serie is uniformly convergent on (-1, 1).  Now I have to find out how I can add the bounds to the interval.  I'm able to show that the serie is convergent on x=1 and x=-1.  Is this sufficient to have uniform convergence on the whole interval [-1, 1] ?  If so, how to prove it?  Thank you.
Edit : We've seen a theorem (which is Abel's theorem) that says that if the power serie converges with x = R, then it is uniformly convergent on [-r,R] (assuming it is centered in 0) for any 0 < r < R.  That would imply that my serie is uniformly convergent on (-1, 1].  But I can't use it for x = -1.
Edit 2 : Abel's theorem states that if the serie of anR^n converges, then the serie is uniformly convergent on [0, R].  Can we say the same with -R?

It is the same for $-R$ since you can adapt the signs of the coefficients properly s.t. the new power series is convergent at $R$. 
