Hello, ggcoralysp!

Let's baby-talk our way through this . . .A rubber ball is dropped from height 10 meters.

If it rebounds aprox 1/2 the distance after each fall, use geometric series

to approximate the total distance that the ball travels before coming to rest.

The ball falls 10 meters: .

It bounces up 5 meters and falls 5 meters: .

It bounces up meters and falls meters: .

It bounces up meters and falls meters: .

It bounces up meters and falls meters: .

. . and so on . . .

The total distance is: .

.[1]

The geometric series has: .first term , common ratio

. . Its sum is: .

Substitute into [1]: . meters.