题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-99290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-47234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-13969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055328-62282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055328-21556.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055328-53949.png)
(2)设数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055328-55358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-47234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055328-18899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055329-85212.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055329-24029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055329-93619.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-47234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055329-71629.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-18648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-61604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-47234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-33051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-53927.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-33422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055331-45272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055331-21107.png)
解析
试题分析:(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055329-24029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055329-93619.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-47234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055331-45951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055331-65326.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055332-25343.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-18648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-61604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055327-47234.png)
所以数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-33051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-53927.png)
(2)由(1)得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-18648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055332-34038.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055332-19121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055332-38440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055330-33422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055331-45272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055332-50454.png)
点评:中档题,本题具有较强的综合性,本解答从确定通项公式入手,认识到数列的特征,利用“裂项相消法”达到求和目的。“分组求和法”“裂项相消法”“错位相减法”是高考常常考到数列求和方法。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-74119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-54109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-35836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-28150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-34499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-50057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-42237.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-74119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-28150.png)
(2) 记
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-52121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-36029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-87837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-18783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-32332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-14453.png)
(1)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-32332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-93537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-82736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-19197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-98923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055236-68545.png)
(2)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-32332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-18783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-26199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-21277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-83758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-66453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-26199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-98105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055215-14784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055215-72867.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055207-29511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055207-97750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055207-34416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055208-38449.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055151-20401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055151-42943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055152-69768.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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