∵|a-1|+|ab-2|=0
∴a-1=0 ab-2=0
∴a=1 b=2
∴原式=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2015×2016)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2015-1/2016
=1-1/2016
=2015/2016