题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-45007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-26231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-54851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-94891.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-45007.png)
(2) 设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-18402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-54851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-57857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-45968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-98362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-54851.png)
成立?若存在,求出
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-45968.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-42827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-24803.png)
解析
试题分析:本题主要考查等差数列的证明、等差数列的通项公式、累加法、裂项相消法等基础知识,考查学生的分析问题解决问题的能力、转化能力、计算能力.第一问,将
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-67033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-50937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140033-40762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-42827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140033-70954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-57857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-24803.png)
试题解析:(1)(解法一)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-94891.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140033-44535.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140033-67068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140034-99563.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-50937.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140034-41948.png)
两式相减得
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140034-62130.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140034-32936.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140035-95631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140033-40762.png)
∴ 数列
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-45007.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-26231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140035-48618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140035-95975.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-42827.png)
(解法二) ∵
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-94891.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140033-44535.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140033-67068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140036-15208.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-50937.png)
等式两边同时除以
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140036-44613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140036-94526.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140036-14596.png)
累加得
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140037-42489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140037-46816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140037-80218.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-42827.png)
(2) 由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-42827.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140037-28374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140038-81823.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140038-96450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140038-73226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140038-76714.png)
则要使得
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-98362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-54851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140039-14853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140039-31083.png)
∴ 存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-45968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-98362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140030-54851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140031-45968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008140032-24803.png)
核心考点
试题【已知数列中,,前项和.(1) 求数列的通项公式;(2) 设数列的前项和为,是否存在实数,使得对一切正整数都成立?若存在,求出的最小值;若不存在,请说明理由.】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
(1)求数列{an}的通项公式;
(2)若数列{bn}满足bn=an+1+log2an(n=1,2,3,…),求数列{bn}的前n项和Sn.
(1)求数列{an}的通项公式;
(2)若数列{an}的前k项和Sk=-35,求k的值.
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135726-50223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135726-51741.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135549-84035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135550-35205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135550-24025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135550-94830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135550-11587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135527-45726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135527-26007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135527-88387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135527-69739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135527-59876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191008/20191008135528-29291.png)
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