1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+.+1/98*99+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/98-1/99+1/99-1/100
=1-1/100
=99/100