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解方程1/(x+1)(x+2)+1/(x+2)(x+3)+......+1/(x+2005)(x+2006)=1/2x+4012

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3 | 2009-7-30 22:16:42 | 显示全部楼层 |阅读模式

1/(x+1)(x+2)+1/(x+2)(x+3)+......+1/(x+2005)(x+2006)=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+......+1/(x+2005)-1/(x+2006)=1/(x+1)-1/(x+2006)=2005/(x+1)(x+2006)即原式化为：2005/(x+1)(x+2006)=1/2（x+2006）解得x=4009...

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千问 | 2009-7-30 22:16:42 | 显示全部楼层

1/(x+1)(x+2)+1/(x+2)(x+3)+......+1/(x+2005)(x+2006)=1/(2x+4012)1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+......+1/(x+2005)-1/(x+2006))=1/(2x+4012)1/(x+1)-1/(x+2006)=1/(2x+4012)2005/(x+...

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