(1/1×2+1/2×3+1/3×4+……+1/2011×2012)x=2011
(1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012)x=2011
(1-1/2012)x=2011
2011/2012×x=2011
x=2012