AP Calculus BC glossary
Conditional convergence
A series converges conditionally when it converges as written but the series of its absolute values diverges. The cancellation between positive and negative terms is what makes it work, so the convergence depends on the order of the terms.
The deciding procedure is two tests, not one: apply the alternating series test to the original series, then test the absolute values separately. Convergent plus divergent means conditional; convergent plus convergent means absolute.
The alternating harmonic series is the standard example, converging to while its absolute values form the divergent harmonic series.
Appears in: Unit 10: Infinite Sequences and Series (BC)