ab-2的绝对值与b-1的绝对值互为相反数求1/ab+1/a+1*b+1+1/(a+2)(b+2)+……+1/(a+2012)(b+2012

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ab-2的绝对值与b-1的绝对值互为相反数求1/ab+1/a+1*b+1+1/(a+2)(b+2)+……+1/(a+2012)(b+2012

由题得:|ab-2|+|b-1|=0,得出:b=1,a=2
1/ab+1/[(a+1)*(b+1)]+1/[(a+2)(b+2)]+……+1/[((a+2012)(b+2012)]
=1/2+1/2*3+1/3*4+.+1/(2013*2014)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2013-1/2014)
=1-1/2014
=2013/2014