## Infinite Number of circles

On a straight line , we have an infinite sequence of circles Γn, each with radius 12n, such that Γn is externally tangential to the circles Γn1,Γn+1 and the line . Consider another infinite sequence of circles Cn, each with radius rn, such that Cn is externally tangential to Γn,Γn+1 and . The expression i=1ri can be expressed as ab, where a and b are positive integers. What is the value of a+b?