题目
题型:不详难度:来源:
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042136-46898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042136-94268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-16073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-23841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-99005.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042136-46898.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-28838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-28838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-97275.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-41409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-97275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-97275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-86803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-93126.png)
化简得:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-98471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-62182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-99510.png)
解析
试题分析:(1) 解:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042139-59963.png)
∴ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042139-85794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042139-83728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042139-77838.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042139-94529.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042140-85297.png)
② - ①得:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042140-78158.png)
以下提供两种方法:
法1:由③式得:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042140-39317.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042140-85864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042141-67824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042141-54112.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042141-86933.png)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042141-28352.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042141-17190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042142-88889.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042142-39636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042142-98016.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042142-46229.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-41409.png)
法2:由③式得:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042142-76534.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042143-92284.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042142-39636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042143-52302.png)
⑤-④得:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042143-90375.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042143-91290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042143-71140.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042144-87651.png)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042136-46898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042139-77838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-41409.png)
(2)解:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-28838.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042144-32699.png)
假设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-97275.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042144-57944.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-93126.png)
化简得:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-98471.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-62182.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042138-99510.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042137-97275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042136-94268.png)
点评:本题需要构造新数列,难度很大,求解中用到的关系式
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042144-80777.png)
第二问中的反证法的应用比综合法分析法更简单实用;本题还考查了合情推理、化归与转化、特殊与一般的数学思想方法,以及抽象概括能力、推理论证能力、运算求解能力
核心考点
试题【(本小题满分14分)已知数列的前项和为,且 N.(1) 求数列的通项公式;(2)若是三个互不相等的正整数,且成等差数列,试判断是否成等比数列?并说明理由. 】;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/20191015/20191015042124-12346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042124-99453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042124-17577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042125-93801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042125-12297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042125-10630.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042124-12346.png)
(Ⅱ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042125-71833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042125-84129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042124-99453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042125-71833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042113-39114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042114-53195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042114-69383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042114-91256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042114-35941.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042115-41071.png)
(Ⅱ)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042115-70561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042114-69383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042115-65126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042115-36032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042105-74737.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042056-95790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042056-77317.png)
(I)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042056-95790.png)
(II)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042056-95790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042056-36121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042056-77773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042048-57924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042048-29398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042048-57484.png)
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