题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201614-45612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201614-16728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-71032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-63087.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-63925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-99968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-47260.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-64755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-63925.png)
答案
解析
试题分析:
(1)根据题意
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-63925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-40764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-57751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-99968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-29787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-23484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-58953.png)
(2) 根据
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-64755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-73943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-84488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-71032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-64463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201618-14874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201618-24230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-63925.png)
试题解析:
由题意可知
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201618-86769.png)
(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-63925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-40764.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-99968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201618-75036.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201619-12533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201619-87364.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201619-97055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201619-86606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201620-68638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201620-88250.png)
从而对于所有的
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201620-77557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201621-94648.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201616-64755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201621-11146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-73943.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-84488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-71032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201621-40635.png)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201621-24997.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201622-46758.png)
则对于所有的
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201621-40635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201617-64463.png)
在(*)式中分别取
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201618-14874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201622-47364.png)
从而有
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201622-86029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201622-99846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201622-11289.png)
由②③得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201623-85998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201623-47106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201623-66045.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201623-26762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201623-66045.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201624-94857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201624-85833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201624-40247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201624-53811.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201623-66045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201615-63925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201625-59777.png)
核心考点
举一反三
A.0 |
B.3 |
C.8 |
D.11 |
A.-48 |
B.-40 |
C.-49 |
D.-43 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201304-92526.png)
A.3 |
B.4 |
C.5 |
D.6 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201259-90951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201300-36010.png)
A.2n |
B.2n-1 |
C.2n+1或3 |
D.2n-1或3 |
(1)求数列{an}的通项公式;
(2)求数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011201238-62796.png)
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