1/1×3+1/3×5+1/5×7 +1/2007×2009

问题描述:

1/1×3+1/3×5+1/5×7 +1/2007×2009

1/1×3+1/3×5+1/5×7 +……+1/2007×2009
=(1-1/3+1/3-1/5+1/5-1/7+……+1/2007-1/2009)/2
=(1-1/2009)/2
=1004/2009