题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203310-61768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203310-50522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203310-60260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203311-13976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203311-11164.png)
答案
解析
试题分析:根据已知不等式猜想第n个不等式,然后利用数学归纳法证明即可.
试题解析:解:根据给出的几个不等式可以猜想第
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203311-66206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203311-43451.png)
用数学归纳法证明如下:
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203312-21852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203310-61768.png)
(2)假设当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203312-43759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203312-38703.png)
则当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203312-44952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203313-78484.png)
即当
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203312-44952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203313-20387.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203254-89928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203254-38517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203255-56145.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203255-80308.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203255-88392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203205-10706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203205-13872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203205-18116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203205-10706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203132-55189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203132-15602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203132-88820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203132-36347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203133-20339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203133-15847.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203132-88820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203133-92032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203133-15847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203133-26736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203022-54160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203022-66745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203023-30214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203002-12710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203002-78693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203002-48159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203003-92522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203003-38267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203003-33479.png)
(Ⅰ)用
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203003-92522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203003-39615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203004-87922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203004-15570.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203004-14152.png)
(Ⅲ)求证:对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200206/20200206203004-92665.png)
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