I now how to workout this problem, but I make a few small errors along the way and I need some sort of checking or help.

Problem.

A ball is drooped from a height of 10 feet (Assume no air resistance), each bounce is of the height of the bounce before. Thus, after the balls hit the floor for the first time, the ball rises to a height of , after the second time, .

A. Find an expression for the height which the ball rises

Problem. after it hits the floor for the nth time.

Thus, , ,

B. Find an expression for the total vertical distance the ball has travled for the first, second, third, and fourth times.

D. Find the closed form expression for the total distance traveled for the nth time, this the part where I get my confused in properly making a simplify formula and simplifying it