计算:(1-1/2-1/3-1/4-1/5)乘以(1/2+1/3+1/4+1/5+1/6)-(1-1/2-1/3-1/4-1/5-1/6)乘以(1/2+1/3+1/4+1/5)的结果是__________.

问题描述:

计算:(1-1/2-1/3-1/4-1/5)乘以(1/2+1/3+1/4+1/5+1/6)-(1-1/2-1/3-1/4-1/5-1/6)乘以(1/2+1/3+1/4+1/5)的结果是__________.

原式=(1-1/2-1/3-1/4-1/5)*(1/2+1/3+1/4+1/5)+1/6*(1-1/2-1/3-1/4-1/5)
-(1-1/2-1/3-1/4-1/5)*(1/2+1/3+1/4+1/5)+1/6*(1/2+1/3+1/4+1/5)
=1/6*(1-1/2-1/3-1/4-1/5+1/2+1/3+1/4+1/5)
=1/6*1
=1/6