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
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 16:46:46
![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](/uploads/image/z/34902-54-2.jpg?t=%E8%AE%A1%E7%AE%97%3A19%C3%9721%2F1%2B21%C3%9723%2F1%2B23%C3%9725%2F1%E2%80%A6%E2%80%A6%2B97%C3%9799%2F1%E9%83%BD%E6%98%AF1%E5%9C%A8%E4%B8%8A%E9%9D%A2..8%E5%A5%BD%E6%84%8F%E6%80%9D...%E5%BA%94%E8%AF%A5%E6%98%AF%3A1%2F19%C3%9721%2B1%2F21%C3%9723%2B1%2F23%C3%9725%E2%80%A6%E2%80%A6%2B1%2F97%C3%9799)
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)