规定a□b=(b-a)/(ab),求1□2-2□3 - 知识问答

规定a□b=(b-a)/(ab),求1□2-2□3-3□4.-2012□2013

1个回答

n□(n+1)=[(n+1)-n]/n(n+1)
=1/n(n+1)
=1/n-1/(n+1)
所以原式=1/1*2-(1/2*3+1/3*4+……+1/2012*2013）
=1/2-(1/2-1/3+1/3-1/4+……+1/2012-1/2013)
=1/2-(1/2-1/2013)
=1/2013

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