1/1*2+1/2*3+1/3*4+.+1/98*99+1/99*100
=[1-1/2]+[1/2-1/3]+[1/3-1/4]+.+[1/98-1/99]+[1/99-1/100]
=1-1/2+1/2-1/3+1/3-1/4+.+1/98-1/99+1/99-1/100
=1-1/100
=99/100