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:学生作业学帮网 编辑:学帮网 时间:2024/05/15 04:16:22

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)