[1/2]+[1/3-1/2]+[1/4-1/3]+[1/5-1/4]+…+【1/2011-1/2010]+[1/2012-1/2011]
=1/2+1/3-1/2+1/4-1/3+1/5-1/4+…+1/2011-1/2010+1/2012-1/2011
观察可发现从第一项到最后隔项可消除
=1/2012
计算 [1/2-]+[1/3-1/2]+[1/4-1/3]+[1/5-1/4]+…+【1/2011-1/2010]+[1
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