题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070946-77790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-55250.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-77967.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-70920.gif)
又f(1)=1
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-48998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-77967.gif)
(2)若a1=3,由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070948-68618.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070948-82260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070948-33098.gif)
假设当n≥3时,0<an<1,则0<an+1=
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070948-48868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070948-88242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070949-26065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
另解:由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070949-96510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070949-50806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070949-80578.gif)
∴要满足an<an+1,即
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070950-96725.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070950-64521.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070950-69041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070950-58434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070951-65320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070951-68959.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070951-65320.gif)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070946-77790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-55250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070951-69913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070952-11828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070952-11828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070952-37908.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070952-62866.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070952-27777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070953-26107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070953-12102.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070953-72782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070953-16429.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070951-68959.gif)
另解:由(2)的方法2可得
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070953-80851.gif)
要使0<an<1,则0<
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070954-50572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070954-61680.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070954-58818.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
即当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070954-21493.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070946-77790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-55250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070954-21493.gif)
∴m≤n-2
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070947-15147.gif)
核心考点
试题【(本题满分14分)已知函数f(x)满足2ax·f(x)=2f(x)-1,f(1)=1,设无穷数列{an}满足an+1=f(an).(1)求函数f(x)的表达式;】;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/20191013/20191013070933-10981.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070933-25622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070933-28793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070933-96105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070934-40535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070934-80284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070934-18062.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070919-38791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070919-52030.gif)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070919-38791.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070919-33543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070920-20732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070920-53408.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070920-58045.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070920-23487.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-75708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-15964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-15964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-15964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-15964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-15964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-98753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-43619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-43619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070914-43619.gif)
A.是等差数列但不是等比数列 | B.是等比数列但不是等差数列 |
C.既是等差数列又是等比数列 | D.既不是等差数列也不是等比数列 |
(Ⅰ)求数列{an}的通项公式:
(Ⅱ)若数列{an}和数列{bn}满足等式:an==
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070857-69278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070857-86738.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070857-16866.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013070829-64610.gif)
A.4 | B.5 | C.6 | D.7 |
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