$\"\"$

A ball is dropped from the height of $\"\"$ .

Each time it drops $\"\"$ it rebounds $\"\"$ .

On the first fall of the ball it falls from $\"\"$ .

On the second rebound, the ball travels a distance of $\"\"$ .

On the third rebound, the ball travels a distance of $\"\"$ .

Each time when the ball hits the ground it gets a factor of $\"\"$ , therefore it is geomentric series.

Therefore, the geometric series can be written as $\"\"$ .

$\"\"$

Theorem 9.6:

Convergence of a geomentric series: A geomentric series with ratio $\"\"$ diverges if $\"\"$ , then

series converges to the sum $\"\"$ .

The geomentric series is $\"\"$ .

$\"\"$

The total distance travelled by the ball is $\"\"$ .

$\"\"$

The total distance travelled by the ball is $\"\"$ .