题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033249-64825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033249-58402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033250-92962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033250-48998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033250-96475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033250-13471.png)
(Ⅰ) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033301-73272.png)
(Ⅱ) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033249-64825.png)
(Ⅲ) 证明:对一切正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033249-58402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-57589.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-38685.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-69111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-20173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-89578.png)
(Ⅱ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-72544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-99040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-88526.png)
两式相减得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033303-99849.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033308-33403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033308-92996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033308-74355.png)
故数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033308-67479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033309-59112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033309-31570.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033309-20003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-38685.png)
(Ⅲ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033309-48713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033309-38803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033309-46898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033310-22769.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033310-60460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033310-63483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033310-74939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033311-20913.png)
综上,对一切正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033249-58402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033302-57589.png)
(1)直接将n换为2代入递推式求解;(2)借助
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033311-28308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033308-67479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033311-33341.png)
【考点定位】本题考查数列的通项公式和数列求和问题,以及不等式的证明.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033234-16651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033234-92292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033234-16651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033234-70781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033235-78335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033235-38507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033235-67404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033137-70572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033137-65311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033137-75966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033138-42969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033138-10500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033138-68744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033138-45867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033139-16904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033139-63345.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033139-64056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033139-90298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033139-11325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033140-86550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033140-28687.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033140-62656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033139-64056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033112-16459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033112-23711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033112-81924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033113-53585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033113-37444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033113-66591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033113-52972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033113-15495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033114-31511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033114-54915.png)
(1)求集合
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033120-19614.png)
(2)求集合
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033120-86252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033104-17707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033104-13518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033104-72182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033058-78497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033059-15231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012033059-71895.png)
A.99 | B.100 | C.96 | D.101 |
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