Geometric Series

1. Definition of a Geometric Series

2. Sum of First \(n\) Terms of a GP

2.1. Case \(r \neq 1\)

2.2. Case \(r = 1\)

3. Sum of an Infinite GP

3.1. Condition \(|r| < 1\)

3.2. Formula for Infinite Sum

4. Applications of GP Sum

4.1. Finding Number of Terms

4.2. Finding First Term or Common Ratio

5. Examples

5.1. Simple GP Sum Examples

5.2. Real-Life Applications of GP Series