x/1X2+x/2X3+…+x/2012X2013=2012
x(1/1×2+1/2×3+1/3×4+……+1/2012×2013)=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
x/1X2+x/2X3+…+x/2012X2013=2012
x(1/1×2+1/2×3+1/3×4+……+1/2012×2013)=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