Sum of a geometric series
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
Σₙ₌₀^∞ a·rⁿ = a/(1 − r), |r| < 1
Problem
Find the sum of the infinite geometric series 2 + 1 + 0.5 + … (first term 2, ratio 0.5).
Working
- 1|r| = 0.5 < 1, so the series converges.
- 2S = a/(1 − r) = 2/(1 − 0.5).
- 3S = 2/0.5 = 4.