1995 AIME Problem 1

Square S_{1} is 1\times 1. For i\ge 1, the lengths of the sides of square S_{i+1} are half the lengths of the sides of square S_{i}, two adjacent sides of square S_{i} are perpendicular bisectors of two adjacent sides of square S_{i+1}, and the other two sides of square S_{i+1}, are the perpendicular bisectors of two adjacent sides of square S_{i+2}. The total area enclosed by at least one of S_{1}, S_{2}, S_{3}, S_{4}, S_{5} can be written in the form m/n, where m and n are relatively prime positive integers. Find m-n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.