7/3*4+7/4*5+7/5*6......7/99*100的简算

来源：百度知道 编辑：UC知道 时间：2024/05/29 00:22:05
写出过程

7/3*4+7/4*5+7/5*6......7/99*100
=7*(1/3*4+1/4*5+1/5*6......1/99*100)
=7*(1/3-1/4+1/4-1/5+1/5-1/6+......+1/99-1/100)
=7*(1/3-1/100)
=7*97/300
=679/300

利用拆项，过程如下
7/3*4+7/4*5+7/5*6......7/99*100
=7[1/(3*4)+1/4*5+1/(5*6)......+1/(99*100)]
=7[1/3-1/4+1/4-1/5+1/5-1/6......+1/99-1/100]
=7[1/3-1/100]
=7*(100-3)/300
=679/300

7/3*4=7/3-7/4

=7/3-7/4+7/4-7/5+7/5-7/6.......+7/99-7/100
=7/3-7/100
=(7*100-7*3)/300
=679/300

//原式=7{1/3*4+1/4*5+1/5*6......1/99*100}=
=7{1/3-1/4+1/4-1/5+1/5-1/6......1/99-1/100}
=7{1/3-1/100}
=67

拜托你,是(7/3)*4还是7/(3*4)??