Series/Convegence tests! need help on review problems for test!

1. A certain ball has the property that each time it falls from a 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.

a) Assuming the ball bounces indefinitely, find the total distance that it travels (Use the fact that the ball falls 1/2gt^2 meters in t seconds)

b)calculate the total time that the ball travels

2. A series is Sum an is defined by the equations:

a1 = 1 an+1 = [(2+cosn)/(sqrt(n)]*an

Determine whether Sum an converges or diverges.

could someone show me how to do these? going NUTS.

thank u