作业帮这道题怎么做求简便计算
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/16 18:40:33
这道题怎么做求简便计算
( 1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=[1+(1/2+1/3+1/4)]×(1/2+1/3+1/4+1/5)-[1+(1/2+1/3+1/4+1/5)]×(1/2+1/3+1/4)
=[1×(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)]-
[1×(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)]
=(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-
(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=1/5+0
=1/5
再问： 这么多，完全看不懂😓
再答： 那就算了
=[1+(1/2+1/3+1/4)]×(1/2+1/3+1/4+1/5)-[1+(1/2+1/3+1/4+1/5)]×(1/2+1/3+1/4)
=[1×(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)]-
[1×(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)]
=(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-
(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=1/5+0
=1/5
再问： 这么多，完全看不懂😓
再答： 那就算了