题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-25442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-36573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-49863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-92185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-37441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-43013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-85138.png)
(Ⅰ)写出数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-60178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-33854.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-56896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-85138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-43013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-93615.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-93700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-85138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-43013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-43013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-63736.png)
列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-85138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-43013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-63736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-50114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-31785.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-77800.png)
(Ⅱ)证明: 因为
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-49863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-54352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-54344.png)
……
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-61461.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-56896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-56896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-39508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-88454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045702-97844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045702-85753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045702-91696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-93615.png)
(Ⅲ)证明:对于数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-85138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-43013.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-49863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-54352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-54344.png)
……
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045701-61461.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-56896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-56896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045702-77428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045702-22800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045702-97844.png)
相加得
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045703-68169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045703-87718.png)
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045659-43013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-63736.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045658-49863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045703-26003.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045703-52614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045703-32940.png)
同理可证,
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045704-41446.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045700-31785.png)
解析
核心考点
试题【(本小题满分13分)已知数列.如果数列满足,,其中,则称为的“衍生数列”.(Ⅰ)写出数列的“衍生数列”;(Ⅱ)若为偶数,且的“衍生数列”是,证明:;(Ⅲ)若为奇】;主要考察你对数列综合等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045649-59624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045650-41981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045650-42708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045650-68573.png)
A.b | B.b—a | C.—b | D.—a |
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045638-63627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045638-98600.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045638-63627.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045638-31050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045639-23626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045629-83315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045629-41221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045629-45132.png)
(I)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045629-83103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045629-49856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045612-96753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045602-16190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045602-65334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045603-37099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045603-95554.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045603-94153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045602-16190.png)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045603-15567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045604-98560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015045603-15567.png)
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