题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041347-32356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041347-39711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041347-40205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041348-33111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041348-10888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041348-23038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041348-44647.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041347-32356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041348-10888.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-13426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-24206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-10030.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-84974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-16191.png)
(2)通过
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041350-32578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-24206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041350-47333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-10030.png)
解析
试题分析:(1)解:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041347-40205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041350-19343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041350-36364.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041351-16546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041351-25602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041351-12615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041351-25580.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041351-52822.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041347-39711.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-84974.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041348-44647.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041352-68125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041352-88429.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041352-84377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041352-79452.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041353-14533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041352-79452.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041353-66409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041352-79452.png)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041348-10888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041353-46474.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041353-95615.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041354-44249.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-16191.png)
(2)证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041354-59749.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041354-27971.png)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-24206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041350-47333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041349-10030.png)
点评:中档题,利用已知条件,布列方程组,先求出数列的通项,从而根据数列通项的特点选择合适的求和方法。“分组求和法”“裂项相消法” “错位相减法”是常常考到的求和方法。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041334-58856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041334-76470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041334-35602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041334-60679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041335-65162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041335-36371.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041335-91170.png)
(2)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041334-58856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041325-75646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041325-32497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041326-98940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041326-58933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041326-36458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041326-15974.jpg)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041317-19190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041317-51249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041317-98048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041317-72284.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041318-83941.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041318-82188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041318-20164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041318-51044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041319-32799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041310-79247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041310-15686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041311-91183.png)
A. 10 | B. 15 | C. 20 | D. 25 |
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041305-31648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041305-87481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041306-10775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041306-12231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041306-64313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041306-89905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015041307-37378.jpg)
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