A ball is dropped from a height of 5m. Each time it hits the ground, it rebounds to 60% of the height from which it fell. The bounces continue indefinitely until the ball comes to rest.
a. (i) Write a mathematical expression for the total vertical distance travelled by the ball (downward and upward together) after infinitely many bounces.
b. (ii) Show that the expression obtained in part (i) represents a convergent series.
c. (iii) Find the exact total distance travelled by the ball to the nearest centimetre.