Uniform Convergence Proof

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

If Σ_{k=0infinity }a_{k} converges absolutely, prove that Σ_{k=0infinity }a_{k}x^{k }converges uniformly on [-1,1]

Since this is a power series, I thought I'd go the approach that if a_{k}x^{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.

Re: Uniform Convergence Proof

It's simple: the remainder $\displaystyle \left|\sum_{k=N}^\infty a_kx^k\right| \le \sum_{k=N}^\infty \left|a_kx^k\right| \le \sum_{k=N}^\infty \left|a_k\right| < \varepsilon$ for a sufficiently large N.