分数巧算1 1 1 1 1——+-------+---------- + ------------+------------ 1*2 1*2*3 1*2*3*4 1*2*3*4*5 1*2*3*4*5*6
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 22:53:21
![分数巧算1 1 1 1 1——+-------+---------- + ------------+------------ 1*2 1*2*3 1*2*3*4 1*2*3*4*5 1*2*3*4*5*6](/uploads/image/z/10761350-14-0.jpg?t=%E5%88%86%E6%95%B0%E5%B7%A7%E7%AE%971+1+1+1+1%E2%80%94%E2%80%94%2B-------%2B----------+%2B+------------%2B------------+1%2A2+1%2A2%2A3+1%2A2%2A3%2A4+1%2A2%2A3%2A4%2A5+1%2A2%2A3%2A4%2A5%2A6)
分数巧算1 1 1 1 1——+-------+---------- + ------------+------------ 1*2 1*2*3 1*2*3*4 1*2*3*4*5 1*2*3*4*5*6
分数巧算
1 1 1 1 1
——+-------+---------- + ------------+------------
1*2 1*2*3 1*2*3*4 1*2*3*4*5 1*2*3*4*5*6
分数巧算1 1 1 1 1——+-------+---------- + ------------+------------ 1*2 1*2*3 1*2*3*4 1*2*3*4*5 1*2*3*4*5*6
原式=1/(1*2)+1/(1*2*3 )+1/(1*2*3*4)+1/(1*2*3*4*5)*(1+1/6)
=1/(1*2)+1/(1*2*3 )+1/(1*2*3*4)+1/(1*2*3*4*5)*7/6
=1/(1*2)+1/(1*2*3 )+1/(1*2*3*4)+1/(1*2*3*4)*7/(5*6)
=1/(1*2)+1/(1*2*3 )+1/(1*2*3*4)*[1+7/(5*6)]
=1/(1*2)+1/(1*2*3 )+1/(1*2*3*4)*[37/(5*6)]
=1/(1*2)+1/(1*2*3 )+1/(1*2*3)*[37/(4*5*6)]
=1/(1*2)+1/(1*2*3 )*[1+37/(4*5*6)]
=1/(1*2)+1/(1*2*3 )*[157/(4*5*6)]
=1/(1*2)+1/(1*2)*[157/(3*4*5*6)]
=1/(1*2)*[1+157/(3*4*5*6)]
=637/(1*2*3*4*5*6)