Existence of Interval of Convergence of Power Series/Corollary 1

Corollary to Existence of Interval of Convergence of Power Series
A power series converges absolutely at all points of its interval of convergence with the possible exception of its end points.

At the end points nothing can be said: it could be absolutely convergent, or conditionally convergent, or divergent.

Proof
Follows directly from Existence of Interval of Convergence of Power Series.