AP Calculus BC glossary

Convergence

Also called: Divergence, Convergent, Divergent

A series converges when its sequence of partial sums approaches a finite limit, and diverges when it does not. Divergence covers both partial sums that grow without bound and ones that oscillate without settling.

Convergence is a property of the tail, not the front. Changing or removing finitely many terms cannot change whether a series converges, though it does change the sum.

Say which

On free response, a bare claim of convergence earns nothing. Name the test, verify its conditions, and state the conclusion.

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