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(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5

来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/11/18 07:14:17
(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)=
简便.算法
(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5
设A=1/2+1/3+1/4+1/5 B=1/2+1/3+1/4+1/5+1/6
原式=(1+A)×B-(1+B)×A
=B+A×B-A-A×AB
=B-A
=(1/2+1/3+1/4+1/5+1/6)-(1/2+1/3+1/4+1/5 )
=1/6