I need help with the Calculus Question Infinite Series

Question

A pendulum is released and swings until it stops. If it passes through an arc of 15 inches the first pass, and if on each successive pass it travels 3/5 the distance of the preceding pass, how far will it travel before stopping?

Answer 1

Total distance = 15 + 15(3/5) + 15(3/5)² + ...

This is a geometric series with common ratio r = 3/5. Since r lies in the interval (-1,1), the series has a finite sum, S.

S = a₁ / (1-r) = 15 / (1-3/5) = 15(5/2) = 75/2 = 37.5"