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): $\S 15.2$