1/1*2+1/2*3=2^2/2*3=4/6
1/1*2+1/2*3+1/3*4=3^2/3*4=9/12
1/1*2+1/2*3+1/3*4+...1/1997*1998=1997^2/1997*1998=3988009/3990006