AP Calculus BC glossary
nth term test
Also called: Divergence test, Test for divergence
The nth term test says that if the terms of a series do not approach zero, the series diverges. It can only ever prove divergence, because terms approaching zero says nothing about whether the series converges.
It is the cheapest test, so it is worth running first. If the limit of the terms is anything other than zero, you are done in one line.
The mistake
Concluding convergence when the limit is zero. The harmonic series has terms going to zero and diverges anyway, so a zero limit means the test is inconclusive and you need another one.
Appears in: Unit 10: Infinite Sequences and Series (BC)