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