precalculus math help

Question

A hard rubber ball is dropped from a roof of a building that is 4 meters high. The ball rises to 40% of the height from which it fell after each bounce. What is the total vertical distance that the ball had traveled by the time it hit the ground for the 10th time? 

Answer 1

Total distance S = h + 2(04h + 0.16 h + ...+ 0.4⁹h) = h(1 + 2h(0.4 + 0.4² + ...+ 0.4⁹))

Now we use geometric sequence formula: S₉ = 0.4(1 - 0.4⁹)/(1 - 0.4) = 0.6665

So S = 4(1 + 2·0.6665) = 9.332 m

Answer 2

Solved above.