Indian Institute of Foreign Trade 2018 Solved Paper

Let ${\mathit{S}}_1$ be a square of side 4 cm.Circle ${\mathit{C}}_1$ circumscribes the square ${\mathit{S}}_1$ such that all its corners are on ${\mathit{C}}_1$ Another square ${\mathit{S}}_2$ circumscribes the circle ${\mathit{C}}_1$, Circle ${\mathit{C}}_2$ circumscribes the square ${\mathit{S}}_2$ and square ${\mathit{S}}_3$ circumscribes circle ${\mathit{C}}_2$, & so on . If ${\mathit{A}}_{\mathit{N}}$ is the area between the square ${\mathit{S}}_{\mathit{N}}$ and the circle ${\mathit{C}}_{\mathit{N}}$, where N is the natural number. then the ratio of sum of all ${\mathit{A}}_{\mathit{N}}$ to ${\mathit{A}}_{\mathit{l}}$ is