1:1*2+1:2*3+...+1:19*20

1/1*2 +1/2*3 +....+1/19*20=1-1/1*2+1/1*2-1/2*3 +......+1/18*19-1/19*20=
=1-1/19*20=379/380
1/1*2=1- 1/1*2
1/2*3=1/1*2-1/2*3
...........................
1/19*20=1/18*19 -1/19*20