Is this true?
Yes, it is true. I think that implies
Then I guess you just prove converges for x in [0,1).
So B = lim sup |an|^(1/n) = lim sup |1|^1/n = 1. So radius of convergence R = 1/1 = 1. Thus converges for (-1,1). Since [0,1) is a subset of (-1,1), I should converge in that interval.
Is this valid?