题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165600-50995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165600-51219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-74447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-94132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-24793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-70408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-84084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-64229.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165600-50995.png)
(2)是否存在正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-71733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-33649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-71733.png)
的最大值;若不存在,请说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-66767.png)
解析
试题分析:
(1)解法一:根据
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-24793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-67237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-84084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-50588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-66126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-51665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-77634.png)
解法二:根据
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-24793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-67237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-84084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-50588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-82526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-76844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-73534.png)
(2)根据(1)的结论可知,数列是等比数列,所以可以得到其前
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-11999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-33649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-11999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-11999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-11999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-33870.png)
试题解析:(1)解法一:因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-24793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-67237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-84084.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165606-48533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-50588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-66126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-51665.png)
①-②得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165606-91030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-77634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-66126.png)
又根据①有
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165606-72814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165606-62136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165607-55335.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-66767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165600-50995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165607-46232.png)
解法二: 因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165601-24793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-67237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165602-84084.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165606-48533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-50588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
由此得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165607-54124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165607-37516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165608-68923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-82526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165608-95120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165614-78736.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165614-43371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165615-89253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165615-93529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165615-13779.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165615-73337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165615-57759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165603-66767.png)
(2)根据(1)的结论可知,
数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165600-50995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165607-46232.png)
所以其前
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165605-11999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165616-75512.png)
原问题等价于
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165616-96987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165604-47515.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165616-24526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165616-42750.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165616-24526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165617-47575.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165617-62042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165617-98877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165617-89241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165617-98877.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165616-42750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165618-39676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165618-81403.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165617-98877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165618-66085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165618-13210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165619-83403.png)
所以存在符合要求的正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165616-42750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165619-89956.png)
核心考点
试题【已知数列的前项和为,,是与的等差中项().(1)求数列的通项公式;(2)是否存在正整数,使不等式恒成立,若存在,求出的最大值;若不存在,请说明理由.】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-98291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-98291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-98291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-98291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-26716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-60970.png)
考察下列结论: ①
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-98291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-98291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165351-98291.png)
A.1个 | B.2个 | C.3个 | D.4个 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165303-84718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165304-51311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165304-96980.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165142-31617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165143-32293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165145-50821.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165142-31617.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165145-64730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165145-14656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165146-79973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165146-35087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165120-81742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165120-74086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165000-95902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165000-44663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165000-17550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165000-24180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165001-52430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011165001-80601.png)
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