AP Calculus BC glossary
Endpoint analysis
Endpoint analysis is the step that turns a radius of convergence into an interval of convergence. The ratio test gives no information at the two endpoints, so each one must be substituted in and tested separately with another convergence test.
The two endpoints can behave differently. One may give an alternating series that converges while the other gives a p-series that diverges, which is why the interval can be half open.
The mistake
Reporting the radius and stopping. An interval of convergence is not complete until both endpoints have been tested and included or excluded explicitly.
Appears in: Unit 10: Infinite Sequences and Series (BC)