calculus
posted by Bob .
With power series, is an endpoint convergent if you plug it back into the original series, and get an alternating series that is conditionally convergent?

calculus 
MathMate
The ratio test or the nth root test does not indicate absolute convergence at the endpoints.
In general, the radius of convergence is defined for absolute convergence, so if a test for the endpoint(s) yield a conditional convergence, the radius of convergence remains an open interval, i.e. the endpoints are excluded.
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