可用折分法把分数拆分,再错位相加可求.原式＝1/2（1-1/3）+1/2（1/3-1/5）+1/2（1/5-1/7）+1/2（1/7-1/9）+……+1/2（1/2011-1/2013）=1/2（1-1/3+1/3-1/5+1/5-1/7）+1/7-1/9+……+1/2011-1/2013）=1/2(1-1/2013)=10...