提问题(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)×(1+1/2+1/3+1/4+1/5)

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提问题(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)×(1+1/2+1/3+1/4+1/5)
提问题(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)×(1+1/2+1/3+1/4+1/5)

提问题(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)×(1+1/2+1/3+1/4+1/5)
令a=1/2+1/3+1/4
则原式=(1+a)(a+1/5)-a(1+a+1/5)
=a(1+a)+1/5(1+a)-a(1+a)-1/5a
=1/5(1+a)-1/5a
=1/5+1/5a-1/5a
=1/5

路过,打扰了!见谅!

原式=(1+1/2+1/3+1/4)×(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)=(1/2+1/3+1/4+1/5)×(1+1/2+1/3+1/4-1/2-1/3-1/4)-(1/2+1/3+1/4)=1/5

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