1/3*5+1/5*7+1/7*9.+1/2009*2011
=（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+……+1/2009-1/2011）÷2
=（1-1/2011）÷2
=2010/2011÷2
=1005/2011