# Uniform convergence of series of functions given convergence of coefficients

Prove that if $$\sum{a_n}$$ converges then the series $$\sum{a_nx^n}$$ converges uniformly on [0,1]

I believe that I must use the Weierstrass M-test to show this convergence, but this requires that the series be non-negative. I'm not sure where to go from here

One form of Abel's theorem states that if a power series converges at end-point $$R$$ of its interval of convergence, then it converges uniformly on $$[0,R]$$.
But if this was supposed to be an easy exercise in elementary real analysis, I suspect the intention was to have $$\sum_n a_n$$ converge absolutely, or maybe $$a_n \ge 0$$.