巧算：(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+1/6)(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+1/2+1/3+1/4+1/5+1/6)(1/2+1/3+1/4+1/5)=====

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 08:43:45

巧算：(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+1/6)*(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+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)=====
巧算：(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+1/6)*(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+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)
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巧算：(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+1/6)*(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+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)=====
为方便书写,设1/2+1/3+1/4+1/5=t,则
(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+1/6)*(1/2+1/3+1/4+1/5)
=(t+1)*(t+1/6)-(1+t+1/6)*t
=(t²+1/6t+t+1/6)-(t+7/6)*t
=(t²+7/6t+1/6)-(t²+7/6t)
=t²+7/6t+1/6-t²-7/6t
=1/6

设(1+1/2+1/3+1/4+1/5)=A
(1/2+1/3+1/4+1/5)=B
就是把这两个式子当成一个整体来看

令：(1+1/2+1/3+1/4+1/5)=a；
(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+1/6)*(1/2+1/3+1/4+1/5)
=a(a-1+1/6)-(a+1/6)(a-1)
=a²-a+a/6-a²+a-a/6+1/6
=1/6

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