原式=1/2(2/3×5+2/5×7+22/7×9+...+2/2009×2010)
=1/2(1/3-1/5+1/5-1/7+1/7-1/9+...+1/2009-1/2011)
=1/2(1/3-1/2011)
=1/2×2008/6033
=1004/6033.