题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055215-31793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055215-95319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055215-78165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055215-74831.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055215-31793.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055215-80205.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-13413.png)
解析
试题分析:(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-81063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-72917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-67552.png)
两式相除得:
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055217-33968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055217-86934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-13413.png)
(2)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055217-66406.png)
首先得到
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055217-36911.png)
利用“错位相减法”求得
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055218-30121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055218-70113.png)
即得证.
试题解析:(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-81063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-72917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055216-67552.png)
两式相除得:
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055217-33968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055218-64216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055218-51424.png)
(2)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055217-66406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055218-75385.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055218-30121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055219-11180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055219-71015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055219-45711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055219-26650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055220-54880.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055207-23182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055207-58012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055208-78730.png)
A.![]() | B.1或![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055140-63369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055141-82703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055140-63369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055141-32044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055141-49161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055141-74856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055142-66578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055130-50435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055131-77162.png)
(1)求数列{an}的通项公式(用a1表示);
(2)设a1=1,b1=3,
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055131-67249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055131-79684.png)
(3)在(2)的条件下,求
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055131-77973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055112-18848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055112-93352.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055112-28396.png)
(2)记
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055112-11437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055113-55703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055114-88037.png)
(3)是否存在互不相等的正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055114-94836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055114-94836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191014/20191014055114-38634.png)
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