x(1/1×2+1/2×3+1/3×4+……+1 /2012-1/2013)=2012
x(1-1/2+1/2-1/3+1/3-1/4+……+1/2012-1/2013)=2012
x(1-1/2013)=2012
2012x/2013=2012
∴x=2013