[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