帮忙解道初二数学题

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2 | 2009-8-3 17:56:27 | 显示全部楼层 |阅读模式

1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4) …… 1/(x+2005)(x+2006)=1/2x+40121/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)……+1/(x+2005)-1/(x+2006)=1/2(x+2006)1/(x+1)-1/(x+2006)=1/2(x+2006)同乘2(x+1)(x+2006)2(x+2006)-2(x+1)=x+1
2x+4012-2x-2=x+1
x+1=4010
x=4009

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千问 | 2009-8-3 17:56:27 | 显示全部楼层

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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