题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112622-69217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112622-44932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112622-95103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112633-56053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112634-53464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112634-60774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112634-78978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112634-97814.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112634-29959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112622-69217.png)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-17035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-12421.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-30111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-59734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-42191.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-51588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-30763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-21537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-16104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-68745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-99631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-30111.png)
(2) 类比(Ⅰ)中a2的求法,可知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-49028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-33892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112638-67782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-59734.png)
(3) 分两种情况:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112638-63208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112638-76465.png)
解:(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-51588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-30763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-21537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-16104.png)
又∵对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-68745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-99631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-30111.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112638-26437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-30111.png)
(Ⅱ)由(Ⅰ),
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112639-43820.png)
∵对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-68745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-99631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-49028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112639-43990.png)
∵对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-68745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-99631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112637-33892.png)
由此可得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112638-67782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112635-59734.png)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112638-63208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112639-85160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112639-27252.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112640-59753.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112638-76465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112640-54378.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112636-42191.png)
核心考点
试题【(本小题满分14分)设数列是首项为0的递增数列,, 满足:对于任意的总有两个不同的根. (Ⅰ)试写出,并求出; (Ⅱ)求,并求出的通项公式;(Ⅲ)设,求.】;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/20191012/20191012112615-55832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112615-27560.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112555-75613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112555-32343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112555-47314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112555-30356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112555-47314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112537-39876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112537-65742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112537-94764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112537-49611.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112537-39876.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112538-92412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112538-29012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112538-35844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112538-48812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112520-47051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112520-71497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112520-47051.png)
(II)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112520-30460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112520-82226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112521-99078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112521-87665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112521-50724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112521-60343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112509-29666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112509-64633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112509-50640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112509-82076.png)
(2) 猜想数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012112510-64043.png)
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