Question
Paragraph: Let M= \ (x, y) R R : x^ 2 +y^ 2 r^ 2 \ , where r>0 . Consider the geometric progression a_ n = 1 2^ n-1 , n=1,2,3, . Let S_ 0 =0 and, for n 1, let S_ n denote the sum of the first n terms of this progression. For n 1, let C_ n denote the circle with center (S_ n-1 , 0 ) and radius a_ n , and D_ n denote the circle with center (S_ n-1 , S_ n-1 ) and radius a_ n . Question: Consider M with r= 1025 513 . Let k be the number of all those circles C_ n that are inside M. Let l be the maximum possible number of circles among these k circles such that no two circles intersect. Then