10.7 Alternating Series Test for Convergence

Definition: Alternating Series Test

For a series \(\sum (-1)^n a_n\) (where \(a_n > 0\)), the series converges if:

1. \(\lim_{n \to \infty} a_n = 0\)

2. \(a_{n+1} \le a_n\) (The terms are non-increasing in magnitude).