分数巧算1 1 1 1 1——+-------+---------- + ------------+----------
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
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
赞 芙蓉眉眉 幼苗
共回答了30个问题采纳率：90% 举报
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)
=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)
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