A rubber ball falls from an initial height of 10m; whenever it hits the ground, it bounces up 2/3 of the previous height. What is the total distance covered by the ball before it comes to rest?

The distance is 

10+2(10(\frac{2}{3})+10(\frac{2}{3})^2+10(\frac{2}{3})^3+...)

In brackets is a geometric series with ratio \frac{2}{3} and first

Term \frac{20}{3}  its sum is \frac{\frac{20}{3}}{1-\frac{2}{3}}=20  for a distance of 10 + 2(20) = 50 m.

50m is the total distance covered by the ball before it comes to rest