On a straight line ℓ, we have an infinite sequence of circles Γn, each with radius 12n, such that Γnis externally tangential to the circles Γn−1,Γn+1 and the line ℓ. Consider another infinite sequence of circlesCn, each with radiusrn, such thatCnis externally tangential to Γn,Γn+1 and ℓ. The expression ∑i=1∞rican be expressed asa−b√, whereaandbare positive integers. What is the value ofa+b?