因为互为相反数的和为0
所以 |ab-2|+|b-1|=0 两个非负数的和为0,这两个非负数都等于0
ab-2=0 且 b-1=0
a=2 , b=1

原式=1/(ab)+1/[(a+1)(b+1)]+1/[(a+2)(b+2)]+……+1/[(a+2010)(b+2010)]
=1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012