题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230348-19959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-79561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-56174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-52205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-91864.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230350-62606.png)
(2)设数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230350-34712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-79561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230350-31001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230350-57291.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-21617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-75694.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-79561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-89832.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-22075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-25946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-79561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-80347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-62219.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-63853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-22583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230353-93306.png)
解析
试题分析:(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-21617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-75694.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-79561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230353-64413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230353-66471.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230353-33606.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-22075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-25946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230349-79561.png)
所以数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-80347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-62219.png)
(2)由(1)得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230351-22075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230354-86821.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230354-11279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230354-45649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-63853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230352-22583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230354-15976.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/20191009/20191009230200-10581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230200-86898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230201-74208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230201-87198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230201-33487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230202-72642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230202-83172.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230200-10581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230201-87198.png)
(2) 记
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230202-98851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230202-28107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230140-36370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230140-72364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230140-87746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230141-85998.png)
(1)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230140-87746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230141-50888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230141-16556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230141-33930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230142-80546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230142-79904.png)
(2)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230140-87746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230140-72364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230127-24871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230127-71484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230128-22534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230128-49503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230127-24871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230128-88069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230128-61379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009230128-56944.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009225849-84316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009225850-71637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009225850-39933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009225850-70361.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009225818-70654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009225818-81716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009225819-45969.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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