Math Is Fun Forum

A ball takes 1 second to hit the ground when dropped. It then takes 90% of this time to rebound to its new height and this continues unil the ball comes to rest.

a) Show that the total time of motion is given by 1 + 2(0.9) + 2(0.0)^2 + 2(0.9)^3 + .....
b) Find Sn for the series in a.
c) How long does it take for the ball to come to rest.

I understand the concept of how 1 + 2(0.9) + 2(0.9)^2 + 2(0.9)^3 + ...

but I dont get how to get section b, the answer should be 19 - 20 x (0.9)^n

???