1/1*2+1/2*3+1/3*4+...+1/1998*1999
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/1998-1/1999)
=1-1/1999
=1998/1999
附：1/n-1/(n+1)=((n+1)-n)/n*(n+1)=1/n*(n+1)