Convergence or Divergence of a Series

Question

A certain ball has the property that each time it falls from height h onto a hard, level surface, it rebounds to a height rh, where 0<r<1. Suppose that the ball is dropped from an initial height of H meters.

(1) Assuming that the ball continues to bounce infinitely, find the total distance that it travels. (Use the fact that the ball falls 0.5g(t^2) meters in t seconds)

2) Calculate the total time the ball travels.

Answer 1

S = h + rh / (1 - r)

S = [h(1 - r) + rh] / (1 - r

S = (h - rh + rh] / (1 - r

S = h / (1 - r)

Time cannot be determined since h is variable.