AP Calculus BC glossary

Interval of convergence

The interval of convergence is the complete set of inputs for which a power series converges. You find the radius with the ratio test, then test each endpoint separately, because the ratio test is inconclusive exactly there.

Endpoint testing is a separate job requiring a different test, usually the alternating series test on one side and a p-series comparison on the other. All four bracket combinations are possible.

The mistake

Reporting the radius and stopping, or assuming both endpoints behave the same way. They very often do not, which is why each is checked on its own.

Appears in: Unit 10: Infinite Sequences and Series (BC)