Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1 . The same process is applied to S2 to form yet another square S3, and so on. If A1,A2,A3,....... be the areas and P1,P2,P3,....... be the perimeters of S1,S2,S3,....... , respectively, then the ratio P1+P2+P3+P4+....A1+A2+A3+A4+.... equals : (CAT 2003)

Let S1 be a square of side a. Another square S2 is formed by joining

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1.	Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1 . The same process is applied to S2 to form yet another square S3, and so on. If A1,A2,A3,....... be the areas and P1,P2,P3,....... be the perimeters of S1,S2,S3,....... , respectively, then the ratio P1+P2+P3+P4+....A1+A2+A3+A4+.... equals : (CAT 2003)
Answer» Let $S_{1}$ be a square of side a. Another square $S_{2}$ is formed by joining the mid-points of the sides of $S_{1}$ . The same process is applied to $S_{2}$ to form yet another square $S_{3}$ , and so on. If $A_{1}, A_{2}, A_{3}, . . . . . . .$ be the areas and $P_{1}, P_{2}, P_{3}, . . . . . . .$ be the perimeters of $S_{1}, S_{2}, S_{3}, . . . . . . .$ , respectively, then the ratio $\frac{P_{1} + P_{2} + P_{3} + P_{4} + . . . .}{A_{1} + A_{2} + A_{3} + A_{4} + . . . .}$ equals : (CAT 2003)

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