When the ball is first dropped, it falls
feet. On the first bounce, it rebounds
feet, which means on the second "drop" it must travel
feet again. On the second bounce, the ball rebounds
feet, and on the third drop falls the same distance. And so on.
So there are two directions to track:
The total distance is the sum of these two:
Recall that for an infinite geometric sum, you have
provided that
. So the total distance traveled by the ball is
Starting with a height of
means the total distance is about 152.42 ft.