Hello, xfyz!

I'll get you started on #1 . . .

Let's baby-talk our way through the first few bounces . . .1. A certain ball has the property that each time it falls from a height

onto a hard, level surface, it rebounds to a height , where

Suppose that the ball is dropped from an initial height of meters.

a) Assuming the ball bounces indefinitely, find the total distance that it travels.

First, it falls meters.

Then it bounces up m . . . and falls m.

Then it bounces up . . . and falls

Then it bounces up . . . and falls

. . and so on . . .

The total distance is: .

. .

The series in paretheses has first term 1 and common ratio

. . Its sum is: .

So we have: .