一道简单的数学题

(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)

2025-05-21 23:22:44

推荐回答（2个）

回答1：

(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)

设A=1/2+1/3+1/4

原式=[1+A][A+1/5]-[1+A+1/5]*A=A+1/5+AA+A*1/5-A-AA-A*1/5
=1/5

原式=1/5

回答2：

设A=1+1/2+1/3+1/4
B=1/2+1/3+1/4+1/5
则原式可转化为：
AB-(A+1/5)(B-1/5)
=AB-(AB-A/5+B/5-1/25)
=AB-AB+(A-B)/5+1/25
=[1-(1/5)]/5+1/25
=6/25