AP Calculus BC glossary
Absolute convergence
A series converges absolutely when the series formed by taking the absolute value of every term still converges. Absolute convergence is stronger than ordinary convergence and always implies it.
The practical use is that it lets you apply tests requiring positive terms, such as the ratio and comparison tests, to a series with mixed signs. Establish absolute convergence and ordinary convergence follows for free.
The ratio and root tests are stated in terms of absolute values, so when they conclude convergence they have proved absolute convergence.
Appears in: Unit 10: Infinite Sequences and Series (BC)