(1)  18/12 + 18/20 + 18/30 + 18/42 + ... + 18/1260 = 18*(1/12 + 1/20 + 1/30 + 1/42 + . . . + 1/1260).



(2)  Every addend in the parentheses is 

      =  =  - 

      =  =  - 

      =  =  - 

      =  =  - 

          . . . . . . . . . . . . . . . . 

      =  =  - 



(3)  Add fractions in n.2, on the left sides and on the right sides.

     On the left side, you will get the sum, which is in parentheses in n.1.

     On the right side, all interior term will cancel each other, and only two extreme terms will survive


        1/12 + 1/20 + 1/30 + 1/42 + . . . + 1/1260 =  -  =  = .



(4)  THEREFORE

        18/12 + 18/20 + 18/30 + 18/42 + ... + 18/1260 =  = .


ANSWER.  The requested sum is equal to  = 5 = 5.5.    ANSWER

18/12 + 18/20 + 18/30 + ... + 18/1260

18(1/12 + 1/20 + 1/30 + ... + 1/1260)

18(1/(3*4) + 1/(4*5) + 1/(5*6) + ... + 1/(35*36)

18*

18*

18*((1/3-1/4) + (1/4-1/5) + (1/5-1/6) + ... + (1/34-1/35) + (1/35-1/36))

18(1/3-1/36) = 6-1/2 = 5.5