Derive geometric series formula

What you'll learn

1. Identify a geometric series and state the first term, common ratio, and number of terms
2. Derive the formula S = a(1 - rⁿ)/(1 - r) using the multiply-and-subtract technique, and explain each step of the derivation
3. Apply the formula to compute the sum of any finite geometric series where r ≠ 1
4. Handle the special case r = 1 correctly (sum = na) and explain why the main formula cannot be used when r = 1
5. Solve real-world problems (savings plans, loan payments, repeated geometric growth) using the geometric series formula

Prerequisites

• Choose equivalent forms to reveal properties