1997+1996*1998/1997*1998-1+1998+1997*1999/1998*1999-1+1999+1

(n+(n-1)(n+1))/(n(n+1)-1)=(n^2+n-1)/(n^2+n-1)=1
1997+1996*1998/1997*1998-1+1998+1997*1999/1998*1999-1+1999+1998*2000/1999*20-1=1+1+1=3