计算:19×21/1+21×23/1+23×25/1……+97×99/1都是1在上面..8好意思...应该是:1/19×21+1/21×23+1/23×25……+1/97×99

计算:19×21/1+21×23/1+23×25/1……+97×99/1都是1在上面..8好意思...应该是:1/19×21+1/21×23+1/23×25……+1/97×99
计算:19×21/1+21×23/1+23×25/1……+97×99/1
都是1在上面..
8好意思...
应该是:1/19×21+1/21×23+1/23×25……+1/97×99

计算:19×21/1+21×23/1+23×25/1……+97×99/1都是1在上面..8好意思...应该是:1/19×21+1/21×23+1/23×25……+1/97×99
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)[(1/19)-(1/99)]
=(1/2)(80/1881)
=40/1881.

原式=2/1*(19/1-21/1+21/1-23/1......+97/1-99/1)
=2/1*(19/1-99/1)
=1881/40

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(1/97-1/99)
=1/2(1/19-1/21+1/21-1/23+1/23+…-1/99)
=1/2(1/19-1/99)