1/3*4=1/12=1/3-1/4
1/4*5=1/4-1-5
……
1/99*100=1/99-1/100
1/3*4+1/4*5+1/5*6+1/6*7+……+1/99*100
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7……+1/99-1/100
=1/3-1/100
=97/300