Indian Institute of Foreign Trade 2014 Solved Paper

Let P${}_1$ be the circle of radius r. A square Q${}_1$ is inscribed in P${}_1$ such that all the vertices of the square Q${}_1$ lie on the circumference of P${}_1$ . Another circle P${}_2$ is inscribed in Q${}_1$ . Another Square Q${}_2$ is inscribed in the circle P${}_2$ . Circle P${}_3$ is inscribed in the square Q${}_2$ and so on. If S${}_{\mathrm{N}}$ is the area between Q${}_{\mathrm{N}}$ and P${}_{\mathrm{N}+1}$,where N represents the set of natural numbers, then the ratio of sum of all sucn S${}_{\mathrm{N}}$ to that of the area of the square Q${}_1$ is: