10.2 Working with Geometric Series

Key Term: Common Ratio (\(r\))

The fixed multiplier between successive terms.

Definition: Geometric Series Test

For the series \(\sum_{n=0}^{\infty} ar^n\):

1. If \(|r| < 1\), the series converges. The sum is \(S = \frac{a}{1-r}\).

2. If \(|r| \ge 1\), the series diverges.