1/19×21+1/21×23+1/23×25……+1/97×99=(1/2)[(1/19)-(1/21)]+(1/2)[(1/21)-(1/23)]+(1/2)[(1/23)-(1/25)]+...+(1/2)[(1/97)-(1/99)]=(1/2)[(1/19)-(1/21)+(1/21)-(1/23)+(1/23)-(1/25)+...+(1/97)-(1/99)]=(1/2)...