题目
题型:不详难度:来源:
在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041136-97963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041136-53575.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041136-55840.gif)
(2)证明:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041137-12548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041136-97963.gif)
(3)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041137-45648.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041137-77967.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041137-96640.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041138-91707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041138-32827.gif)
(2)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041138-29409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041138-13390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041138-34038.gif)
公比为-1的等比数列。 7分www
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041139-16887.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041139-53617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041139-98032.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041139-20145.gif)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041140-25719.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041140-28738.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041140-25719.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041140-86296.gif)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041137-77967.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041120-25694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041120-74568.png)
A.24 | B.39 | C.52 | D.104- |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041111-37862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041111-37862.png)
个是
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041111-16915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041112-96550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041112-55878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041112-49521.png)
则数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041112-76501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041112-55878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041112-35856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041113-20761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041112-55878.png)
生成的所有数中不同的数的个数为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041113-90686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041113-16881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041056-39864.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-55496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-70385.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-86473.gif)
(Ⅰ)证明数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-55496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-35864.jpg)
(Ⅱ)把数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-55496.gif)
数表,当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-14414.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041058-95162.gif)
(Ⅲ)对于(Ⅱ)中的数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041057-55496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041058-77805.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041050-68921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041051-58366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041051-88633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041051-64009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041051-72464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041052-73016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041038-19562.gif)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041039-34878.gif)
②存在实数M,使
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041039-38502.gif)
(I)在只有5项的有限数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041039-48595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041039-77537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041039-16749.gif)
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041040-25071.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041040-66284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041040-81833.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041040-18363.gif)
(III)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041040-27250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041041-86400.gif)
求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013041041-98208.gif)
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