Posted by Bob on Wednesday, September 22, 2010 at 6:12pm.
The ratio test or the n-th root test does not indicate absolute convergence at the end-points.
In general, the radius of convergence is defined for absolute convergence, so if a test for the end-point(s) yield a conditional convergence, the radius of convergence remains an open interval, i.e. the end-points are excluded.
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