The Journal of Online Mathematics and Its Applications, Volume 7 (2007)
Bouncing Balls and Geometric Series, Robert Styer and Morgan Besson
How do we calculate the value of an infinite geometric series 1 + r + r2 + r3 + ···? Here is a classic geometric proof! For more details see trapezoid supplement.
The geometric series proof shown in the mathlet is adapted from one of several found in the outstanding book Proofs Without Words (reference). On the next page, we find the sum of a geometric series by the "repeating decimal method" you probably learned in high school.