计算.2\1x3+2\3x5+2\5x7+...+2\2007X2009
问题描述：
计算.2\1x3+2\3x5+2\5x7+...+2\2007X2009
答
＝1/2(1/1乘3+…1/2007乘2009)=1/2乘2(1-1/3+1/3-1/5+1/5-……+1/2007-1/2009)=1(1-1/2009)=2008/2009
答
裂项求和法因为1/〔n（n+2）〕=1/2〔1/n-1/（n+2）〕所以原式=1-1/3+1/3-1/5+……+1/2007-1/2009=2008/2009