(1+1/16+1/17+1/18)×(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 03:45:58
(1+1/16+1/17+1/18)×(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)=(1+1/16+1/17+1/18)

(1+1/16+1/17+1/18)×(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)=
(1+1/16+1/17+1/18)×(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)=

(1+1/16+1/17+1/18)×(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)=
=[(1+1/16+1/17+1/18)*(1/16+1/17+1/18)+(1+1/16+1/17+1/18)*1/19)]-[(1+1/16+1/17+1/18)*(1/16+1/17+1/18)+(1/19*(1/16+1/17+1/18))]=1/19*[(1+1/16+1/17+1/18)-(1/16+1/17+1/18)]=1/19

19分之1

(1+1/16+1/17+1/18)×(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)
=(1/16+1/17+1/18+1/19)+[(1/16+1/17+1/18)(1/16+1/17+1/18+1/19)-
(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)]
=...

全部展开

(1+1/16+1/17+1/18)×(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)
=(1/16+1/17+1/18+1/19)+[(1/16+1/17+1/18)(1/16+1/17+1/18+1/19)-
(1+1/16+1/17+1/18+1/19)×(1/16+1/17+1/18)]
=(1/16+1/17+1/18+1/19)+(1/16+1/17+1/18)[([1/16+1/17+1/18+1/19-1-1/16-1/17-1/18-1/19]
=1/16+1/17+1/18+1/19+(1/16+1/17+1/18)(-1)
=1/16+1/17+1/18+1/19-1/16-1/17-1/18
=1/19

收起