计算.2\1x3+2\3x5+2\5x7+...+2\2007X2009
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计算.2\1x3+2\3x5+2\5x7+...+2\2007X2009
计算.2\1x3+2\3x5+2\5x7+...+2\2007X2009
计算.2\1x3+2\3x5+2\5x7+...+2\2007X2009
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
=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