我国古代数学名著《九章算术注》的轮割圆术中有:“割之弥细,所失弥少,割之又割,以至于不能割,则与圆合体而无所失矣”它体现了一种无限与有限转化过程.比如在表达式
“…”即代表无限次重复,但原式却是个定值,它可以通过方程
求得
,类似上述过程,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70ec5d6c59e453ecd3476e0a8a75e28.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7b4f9f2d852bcc0dc74d0f112022f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127b177e294b7dbc89375c899fb1b0f9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70ec5d6c59e453ecd3476e0a8a75e28.png)
更新时间:2020-07-01 08:42:31
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【推荐1】从![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
个不同小球(其中
个白球,1个黑球)中取出![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
个球共有
种不同取法,还可换一个角度考虑:若取出
个球全是白球,则有
种不同取法,若取出
个球中含有黑球,则有
种不同取法,从而共有
种不同取法.因此,可以得到组合恒等式:
.请你运用类比推理的方法,可以得到排列恒等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02c0091e4c7ebc83fdc70ba8fc5c901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591b7da02481c28da213e7de2ec22528.png)
____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
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【推荐2】对于问题“已知关于
的不等式
的解集为
,解关于
的不等式
的”,给出一种解法:由
的解集为
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的解集为
.即关于
的不等式
的解集为
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的不等式
的解集为
,则关于
的不等式
的解集为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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