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