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

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 14:33:55

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

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