题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023157-92921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023157-86634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023157-25557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023158-10509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023158-12966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023158-71688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023158-93951.png)
(I)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-33623.png)
(II)若对一切
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-48097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-31894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023158-10509.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-40607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023200-31345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023200-69669.png)
解析
试题分析:解:(1)由题意可知当
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023200-35591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023201-34791.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023201-97563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023201-41723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023201-11736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023202-43614.png)
用(1)式减去(2)式得:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023202-24353.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023202-76148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-40607.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023158-93951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023202-45505.png)
当对一切
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-48097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-31894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023214-31643.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023214-37602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023214-58589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-48097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023200-31345.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023214-35616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023214-84764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023159-48097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023200-69669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023202-43614.png)
综合以上可知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023200-31345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023200-69669.png)
点评:对于数列的通项公式的求解,一般可以通过前n项和与通项公式的关系来解得,也可以利用递推关系来构造特殊的等差或者等比数列来求解。而对于数列的单调性的证明,一般只能用定义法来说明,进而得到参数的范围,属于中档题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023142-77600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023142-56633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023142-58437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023142-83699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023143-13093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023143-99937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023143-55697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023143-54097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023143-14004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023144-90175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023143-54097.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023142-77600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023144-52106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023144-73178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023144-33486.png)
(Ⅱ)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023145-76310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023145-79758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010023145-30507.png)
A.-72 | B.72 | C.36 | D.-36 |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022948-34821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022949-22270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022949-92474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022949-84890.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022948-34821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022949-91968.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022950-60178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022950-58895.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022950-73040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022950-53654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022956-81640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022932-82997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022932-28849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022932-67022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022933-53573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022933-61755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022933-70162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022933-30402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022934-13238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022934-16600.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022934-24503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022934-39161.png)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022934-56133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022833-17283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022834-62442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010022834-71107.png)
A.8 | B.7 | C.6 | D.5 |
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