1/1×3 1/3×5 1/5×7 …… 1/2009×2010等于多少

问题描述:

1/1×3 1/3×5 1/5×7 …… 1/2009×2010等于多少

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.