题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-67335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-87482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-25105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-58344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020950-76149.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
答案
解析
试题分析:取
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020951-53884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020951-83724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020951-24581.png)
依次得到数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-67335.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020951-31071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020952-44567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020952-51410.png)
依次得到数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-87482.png)
由上可知存在
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020952-57159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020952-19760.png)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-25105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020952-59307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-67335.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020949-58344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020953-37389.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020953-40122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020953-89834.png)
…
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020953-65437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020954-83391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020954-28312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020954-83391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020954-32007.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020954-90252.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020932-37998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020932-16907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020932-36827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020932-18788.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020919-99127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020919-24190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020920-54149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020920-70446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020920-11724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020920-86367.png)
(1)求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020920-11724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020921-60003.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020921-17704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020919-24190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020752-35474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020753-73301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020753-36681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020753-10221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020629-82622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020629-86044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020629-84472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020629-94359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020629-18727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020630-94508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020630-82200.png)
(1)求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020630-94508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020630-50578.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020630-96494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020631-61742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009020617-91911.png)
(1)证明:数列{an}中有无穷多项为无理数;
(2)当n为何值时,an为整数?并求出使an<200的所有整数项的和.
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