根据同分子分数,分母大的反而小可知：|1/2011-1/2010|+|1/2010-1/2009||+|1/2009-1/2008|…+|1/3-1/2|+|1/2-1|=1-1/2+1/2-1/3+……+1/2008-1/2009+1/2009-1/2010+1/2010-1/2011=1-1/2011=2010/2011...