Geometric Series - Problem 8

A ball that is bounced returns some percentage of its previous drop, which sets up a geometric sequence. If you can draw the first few bounces, you're on your way to a geometric series that represents a theoretical distance that the ball would travel (in real life, the ball doesn't bounce infinitely, but we can be pretty close.) The trick is that you'll need to represent that the ball has one initial drop, and then each subsequent bounce represents traveling up and down the same distance- that is, multiplying most of your sum by 2. There are multiple correct ways to represent this situation- here we look at a common interpretation of the infinite sum.