1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013
=（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+……+1/2011-1/2013）÷2
=（1-1/2013）÷2
=2012/2013÷2
=1006/2013