(1) suppose a bouncing ball rises each time to 2/3 of the height of the previous bounce. Find the height of the tenth rebound, and the distance traveled by the ball after it touches the ground the tenth time.

Compare this distance with the total distance traveled12. In a water puriication process, one-nth of the impurity is removed in the irst stage. Ineach succeeding stage, the amount of impurity removed is one-nth of that removed in thepreceding stage. Show that if n = 2, the water can be made as pure as youlike, but that ifn = 3, at least one-half of the impurity will remain no matter how many stages are used.