Let C be a circle with centre P0 and AB be a diameter of C. Suppose P1 is the mid point of the line segment P0B,P2 is the mid point of the line segment P1B and so on. Let C1, C2, C3, … be circles with diameters P0 P1, P1P2, P2P3… respectively. Suppose the circles C1, C2, C3,… are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is