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