A blank, square sheet of paper is painted as follows: Step 1 consists of ruling the square into nine smaller congruent squares, and painting the central one. Step 2 consists of applying this process to each of the remaining eight squares (a small central square is painted in each). Step 3 consists of applying this process to each of the 64 remaining small squares, etc. The first two steps are shown. Let A0 be the area of the original square, A*1 be the area that is unpainted after Step 1, A*2 be the area that is unpainted after Step 2, and so on. Show that the decreasing sequence A*0, A*1, A*2,... Is geometric. Is it ever true that An<0.01A*0. Justify your answer.