1/1*2+1/2*3+1/3*4.1/1988*1999+1/1999*2000 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/1998-1/1999)+(1/1999-1/2000) =1-1/2+1/2-1/3+1/3-1/4+.+1/1998-1/1999+1/1999-1/2000 =1-1/2000=1999/2000