1/1x2 =1-1/2;
1/2x3 =1/2-1/3;
1/3x4 =1/3-1/4
……
1/2010x2011 =1/2010-1/2011
X/1×2＋X/2×3＋……＋X/2010×2011
=X[1-1/2+1/2-1/3+……+1/2010-1/2011]
=X（1-1/2011）
=(2010/2011)X =2010
X =2011
1/n(n+1) =1/n -1/(n+1),这是常用的数列求和恒等式.