Question

A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance down the ball has traveled when it hits the ground the fifth time is?

Answer 1

The answer would be simply

10 + 5 + 2.5 + 1.25 + .5625

or

19.3125

Answer 2

This problem can be represented by a geometric series.  The first term is 10, and the common ratio (r) is 1/2.

The formula for the nth sum of this partial series is

           1 - r^n

Sn = -------------

           1 - r

In this case,

             1 - (1/2)^5

S      = -------------------

   5           1 - 1/2

             1 - 1/32            31/32

        = ---------------- = -------------- = 1.9375 meters

                1/2                 16/32