3分之1+15分之1+35分之1+······+2007*2009分之1+2009*2011分之1
=(3分之2+15分之2+35分之2+······+2007*2009分之2+2009*2011分之2)÷2
=(1-1/3+1/3-1/5+1/5-1/7+.-1/2007+1/2007-1/2009+1/2009-1/2011)÷2
=(1-1/2011)÷2
=2010/2011÷2
=1005/2011