题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235839-92301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235839-75978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235839-57751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235839-41284.png)
(Ⅰ) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-36722.png)
(i)求
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-55883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235839-92301.png)
(ii)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-61715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-43906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-41010.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-13784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-71087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-98147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-75324.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-72852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-99461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-41010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-76754.png)
(2) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-43906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-85945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-43906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235843-86513.png)
解析
试题分析:(Ⅰ) 解:(i)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235843-76161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235843-84546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-72852.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235843-29357.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235844-53058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235844-45564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235844-58782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235844-42484.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235843-76161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-99461.png)
(ii)由(i)得:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235844-10993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235845-97188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235845-30259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-76754.png)
(Ⅱ)解:因为对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235839-57751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235845-87009.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-98147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235845-80082.png)
又数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235846-73703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235846-79311.png)
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235841-98147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-43906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235846-56060.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235846-31455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235846-20596.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235847-82782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235847-77339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235847-72312.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235847-26689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235847-18349.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-43906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235842-85945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235840-43906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235843-86513.png)
点评:解决的关键是对于数列的递推关系的理解和运用,并能结合裂项法求和,以及分情况讨论求和,属于中档题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235833-69273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235833-13797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235833-21614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235833-68877.png)
A.2 | B.3 | C.-3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235815-44729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235815-54868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235815-81872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235816-10844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235816-35076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235816-87561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235816-25222.png)
(Ⅰ)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235817-59292.png)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235816-87561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235817-44553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235817-35441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235803-89713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235804-17129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235804-39247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235804-43690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235804-64288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235805-40143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235805-57045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235805-83045.png)
A.5 | B.4 | C.3 | D.2 |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235655-47470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235656-43107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235656-81596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235656-41979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235656-25074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235657-98974.png)
A.13 | B.21 | C.34 | D.55 |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235544-37438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235544-28760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235544-69409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235544-60086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235544-47597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009235544-69409.png)
A.最大值31 | B.最小值31 | C.最大值63 | D.最小值63 |
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