X/1×2 + X/2×3 + X/3×4 + ...+ X/2011×2012 = 2011
X(1/1×2 + 1/2×3 + 1/3×4 + ...+ 1/2011×2012) = 2011
X(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/2011 - 1/2012 ) = 2011
X(1 - 1/2012) = 2011
2011X/2012 = 2011
X = 2012
x除以1x2的积+x除以2x3的积+.+x除以2011x2012=2011