10-11高二下·北京·期中
1 . 图中竖直线段和斜线段都表示通道,并且在交点处相遇,若竖直线段有一条的为第一层,有两条的为第二层,以此类推,竖直线段有
条的为第
层,每一层的竖直通道从左到右分别称为第1通道、第2通道,……,现在有一个小球从入口向下(只能向下,不能向上)运动,小球在每个交点处向左到达下一层或者向右到达下一层的可能性是相同的.小球到达第
层第
通道的不同路径数称为
,如小球到达第二层第1通道和第二层第2通道的路径都只有一种情况,因此
,
.
![](https://img.xkw.com/dksih/QBM/2011/8/27/1570292159561728/1570292164829184/STEM/93fe8cc2-c18d-4f84-8a0a-8cf5344510e1.png?resizew=189)
求:(1)
,
,
;
(2)
,以及小球到达第5层第2通道的概率;
(3)猜想
,并证明;
(4)猜想
(不用证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d675fe30f91266e339af76607564feab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ecff070c8cf7cabf5279cd53169160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641549d022f3ef78daf9e1d4b40eb9ad.png)
![](https://img.xkw.com/dksih/QBM/2011/8/27/1570292159561728/1570292164829184/STEM/93fe8cc2-c18d-4f84-8a0a-8cf5344510e1.png?resizew=189)
求:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c787e40071b2f6910b78ee029f1b270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2b2d903cfd3507b7247e98716faf10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357763bc5c8da0190b0e18af65cadd04.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fbac2c7e0e1ce1f1d8e11f2ab11c85e.png)
(3)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbebe3dc1128e07981dc03703ad2a11.png)
(4)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be3652cf6bdc8ba5f5ae2a66266abe3.png)
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