1/1x3+1/3x5+1/5x7+···+1/2009x2011
=1/2x(1-1/3+1/3-1/5+1/5-1/7+···+1/2009-1/2011)
=1/2x(1-1/2011)
=1/2x2010/2011
=1005/2011为什么=1/2x(1-1/3+1/3-1/5+1/5-1/7+···+1/2009-1/2011)搞不懂诶.....因为：2/1x3=1-1/32/3x5=1/3-1/5而题里是：1/1x3 要想成为：2/1x3 则需做如下变换：(1/2 x 2) x1/1x3=1/2 x 2/1x3