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 Σk=0infinity ak converges absolutely, prove that Σk=0infinity akxk converges uniformly on [-1,1]
Since this is a power series, I thought I'd go the approach that if akxk 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.