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.

$\blacksquare$

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 15.2$