AP Calculus BC glossary
Alternating series test
Also called: Leibniz test
The alternating series test says that a series whose terms alternate in sign converges if the absolute values of its terms decrease and approach zero. Both conditions are needed, and together they are enough.
Verify decrease explicitly rather than assuming it: either show directly or show the corresponding function has a negative derivative.
The test proves convergence only. To decide whether the convergence is absolute or conditional, apply another test to the series of absolute values.
The alternating harmonic series
It has decreasing terms going to zero, so it converges, while the harmonic series of absolute values diverges. That is the definition of conditional convergence.
Appears in: Unit 10: Infinite Sequences and Series (BC)