题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052623-62543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052623-47677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052623-19091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052623-35706.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052623-62543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052624-23400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052624-70560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052623-47677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052624-42994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052624-27060.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052624-21773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052625-44107.png)
解析
试题分析:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052625-47144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052625-31773.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052625-34929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052626-71332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052626-39814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052626-73186.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052626-69047.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052624-21773.png)
(2)证明: ∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052626-74727.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052626-71537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052637-21622.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052625-34929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052637-67981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052638-98107.png)
①-②得:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052638-21556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052648-90852.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052649-35719.png)
此式当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052626-71537.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052649-27246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052649-94548.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052649-20200.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052650-55003.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052625-34929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052655-74802.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052656-42539.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052656-17546.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052656-22480.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052656-51631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052657-43253.png)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052625-44107.png)
点评:中档题,本题综合考查等差数列、等比数列的基础知识,本解答从确定通项公式入手,明确了所研究数列的特征。“分组求和法”、“错位相消法”、“裂项相消法”是高考常常考到数列求和方法。先求和,再利用“放缩法”证明不等式,是常用方法。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052608-44288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052608-58637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052608-42998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052608-44288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052609-89481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052608-42998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052609-89481.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052601-13410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052601-59127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052601-67709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052602-67161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052602-80194.png)
( 1 )求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052601-13410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052602-67161.png)
( 2 )设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052602-40375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052602-67244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052601-59127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052602-96431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052525-65714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052525-52479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052525-55877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052526-17346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052526-72004.png)
(I)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052525-65714.png)
(II)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052525-55877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052514-10465.png)
假设第
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052515-90751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052515-93982.png)
(1)依次写出第七行的所有7个数字(不必说明理由);
(2)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052515-96996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052515-13370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052515-71611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052515-93982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-58184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-39020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-91512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-60652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-58184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-39020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-58184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052448-60289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012052449-31456.png)
则下列结论中错误的是
A.若m=![]() |
B.若a3=2,则m可以取3个不同的值 |
C.若![]() ![]() ![]() |
D.![]() ![]() ![]() |
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