1/2*3+1/3*4+1/4*5+…+1/49*50
=1/2-1/3+1/3-1/4+1/4-1/5+…+1/49-1/50
=1/2-1/50
=12/251+2+3+…+99+100+99+98+97+…+3+2+1=(1+2+……+100)+(1+2+……+100)-100=2×(1+2+……+100)-100=2×[(1+100)+(2+99)+……+(50+51)]-100=2×50×101-100=10100-100=10000