# Existence of Interval of Convergence of Power Series/Corollary 1

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## 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): $\S 15.2$