Starting with the vertices of a square, we construct further points as shown in the figure: is the midpoint of is the midpoint of is the midpoint of and so on. The polygonal spiral path approaches a...

Starting with the vertices of a square, we construct further points as shown in the figure: is the midpoint of is the midpoint of is the midpoint of and so on. The polygonal spiral path approaches a point P inside the square.

(a) If the coordinates of P_n
are (x_n, y_n), show that and find a similar equation for the y-coordinates.

(b)Find the coordinates of P.