题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203608-80377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203609-45159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203609-51524.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203609-89678.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203608-80377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203610-26792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203610-23815.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203610-31450.png)
解析
试题分析:(1)证明:由定义
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203610-83251.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203611-60449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203611-82472.png)
(2)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203611-17986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203611-99441.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203612-31851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203610-26792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203612-55629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203612-49827.png)
①-②得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203612-47287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203613-68513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203610-31450.png)
点评:本题是中档题,考查数列的递推关系式的应用,数列通项公式与数列中最大项的求法,考查计算能力,转化思想,分类讨论的应用.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203544-81136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203544-48789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203544-48451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203544-24320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203545-63916.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203544-81136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203544-48789.png)
(2)记
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203544-81136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203545-27942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203545-30050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203545-69175.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203545-97704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203546-15499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203546-34233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203546-67389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203546-36405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203521-77271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203521-69446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203521-57585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203521-90187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009203521-84254.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202957-94168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202957-32088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202957-18609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202957-64831.png)
A.36 | B.39 | C.42 | D.45 |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202606-38941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202606-49574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202607-92173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202607-51742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202607-40347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202607-61502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202414-75847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202414-74463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009202415-48338.png)
A.17 | B.16 | C.15 | D.14 |
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