题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230237-50491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-39027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-79114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-38803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-38291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-38803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-12032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-70091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-97912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-25123.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-38803.png)
(2)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230240-33091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230240-98613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230240-36201.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230251-71866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230251-33288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230251-39793.png)
解析
试题分析:(1)首先由题设知: 集合
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-67454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-22300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-65783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-26011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-22300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-22621.png)
得到
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-97912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-71437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-61643.png)
通过设等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-38803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-29567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-29567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-41953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230254-60889.png)
根据
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-25123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230254-73024.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-26011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-22300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-22621.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230254-92409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-77226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-28508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-59561.png)
(2)由(1)得到
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-89523.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-68999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230256-88588.png)
试题解析:(1)由题设知: 集合
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-67454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-22300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-65783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-26011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-22300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-22621.png)
由此可得,对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230256-68637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230256-97802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-97912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-71437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-61643.png)
设等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-38803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-29567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-41953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230254-60889.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230239-25123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230256-26879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230257-70670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230254-73024.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-26011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230252-22300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230253-22621.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230254-92409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-77226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-28508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230255-59561.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230238-38803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230251-71866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230251-33288.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230257-67893.png)
于是有
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230257-24791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230257-85793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230258-90985.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230226-34978.jpg)
请你用数列知识归纳:(1)这些图中的数所构成的数列:________;(2)写出与这个魔术关联的一个数列递推关系式:________.
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230221-47530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230221-85315.png)
(1)求a2,a3的值;
(2)证明:不等式0<an<an+1对于任意n∈N*都成立.
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230202-11986.png)
(1)求数列{an}的通项公式及前n项和Sn;
(2)求满足
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230202-84793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230203-15895.png)
(1)若b3=3,求b1的值;
(2)求证数列{bnbn+1bn+2+n}是等差数列;
(3)设数列{Tn}满足:Tn+1=Tnbn+1(n∈N*),且T1=b1=-
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011230150-33980.png)
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