题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085210-59897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085210-71973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085210-40862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085210-94755.png)
(1)试用
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085211-27679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085211-17266.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085211-55294.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085211-87349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-92963.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-79156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-40427.png)
解析
(1)因为由题意结合韦达定理可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-25471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-42617.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-82263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-79156.png)
(2)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-79156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-58662.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-31578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-98814.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085211-87349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085214-26032.png)
故数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-31578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-98814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-98814.png)
从而得到表达式。
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-25471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-42617.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-82263.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-79156.png)
(2)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-79156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-58662.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-31578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-98814.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085211-87349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085214-26032.png)
故数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-31578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-98814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085213-98814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085212-40427.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085156-49107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085156-40943.png)
A. 8 | B. 4 | C.1 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085145-54239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085146-89049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085146-52855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085146-58872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085146-96196.png)
(I)设
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085147-84055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085147-28469.png)
(II)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085145-54239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085147-96601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085133-21217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085133-74559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085133-77182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085133-62517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085134-88616.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085112-13066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085112-53319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085112-18304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085113-87024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085113-18354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085113-21125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085113-48698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085113-88076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085114-87535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085114-45813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014085114-70831.png)
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