题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032354-37957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032354-46976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032355-39057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032355-51569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032355-96145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032355-73334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032355-92374.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032356-69654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032356-98805.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032356-11011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032407-11072.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032407-96147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032407-51897.png)
解析
试题分析:解: (1) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032408-74831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032355-73334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032408-19898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032408-48569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032408-68557.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032355-51569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032408-59611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032409-71930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032409-43299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032409-17005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032409-81321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032410-25406.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032410-68123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032407-96147.png)
(2)证明:由(1)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032410-50535.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032410-58760.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032416-88802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032416-67075.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032416-53991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032417-84777.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032417-63894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032417-81949.png)
另解:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032410-58760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032428-31754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032408-74831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032428-92951.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032429-33519.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032408-74831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032429-27899.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032429-66286.png)
则不等式成立.
点评:求一般数列的问题时,常用的方法是裂变法和错位相减法,本题就用到裂变法。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032345-33485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032345-60017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032345-84370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032346-84454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032346-24424.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032345-33485.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032346-89690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032346-88114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032346-89690.png)
(3)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032346-89690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032345-60017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032346-38795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032328-77630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032328-66683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032328-16469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032329-20729.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032309-15855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032309-26773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032310-35545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032310-81070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032310-38571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032311-52265.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032309-15855.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032311-28482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032311-52265.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032309-26773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032311-54627.png)
②若对一切正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032309-26773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032311-56743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032311-79418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032246-29017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032251-81180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032238-89789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032239-64654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012032239-59036.png)
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