Uniform Convergence Proof

I'm having trouble getting this proof, uniform convergence has always been a hard thing for me.

If Σ_k=0^infinity a_k converges absolutely, prove that Σ_k=0^infinity a_kx^k converges uniformly on [-1,1]

Since this is a power series, I thought I'd go the approach that if a_kx^k converges absolutely for x=1, then it converges uniformly for [-1,1]. I'm not sure this is the right approach though, since I'm having trouble starting.

It's simple: the remainder for a sufficiently large N.