LET S₁ AND S₂ BE 2 CIRCLES OF UNIT RADIUS TOUCHING EACH OTHER EXTERNALLY AND L BE THE DIRECT COMMON TANGENT. A CIRCLE C1 WITH THE RADIUS R1 TOUCHES S₁, S₂ AND LINE L.. SIMILARILY CIRCLES C₂, C₃..........CN ARE THE CIRCLES OF RADIUS R₂, R₃ .....R_N. WHERE THE CIRCLE CR TOUCHES S1, CR-1 AND ONE OF THE DIRECT COMMON TANGENT.

FIND LIM _{N ->infinity}(  1/R₁ +  1/R₂ + ...................+ 1/R_N  ) /  N³