1/(2×3) = (3-2)/(2×3)=3/(2×3) - 2/(2×3)= 1/2 - 1/3

Similarly:1(3× 4) =1/3-1/4.

1/(4×5)= 1/4 - 1/5

By analogy, the original formula can be changed to:

( 1/2 - 1/3)+ ( 1/3 - 1/4)+ ( 1/4 - 1/5)+ ...+ ( 1/2005 - 1/2006)

Unpacked:

1/2 - 1/2006 = 1002 / 2006 = 50 1 / 1003