10.8 Ratio Test for Convergence

Definition: Ratio Test

Let \(L = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|\):

1. If \(L < 1\), the series converges absolutely.

2. If \(L > 1\), the series diverges.

3. If \(L = 1\), the test is inconclusive.