题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033117-49695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-59931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-37719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-85532.png)
(1)证明数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-45016.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033117-49695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033119-95458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033119-72236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033119-71125.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-37719.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033119-69577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-85532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033120-71113.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-45016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033120-85301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033120-63755.png)
解析
试题分析:(Ⅰ)由题设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-37719.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033119-69577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-85532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033120-71113.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033118-45016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033120-85301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033120-63755.png)
(Ⅱ)由(Ⅰ)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033120-91865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033117-49695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033121-72934.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033117-49695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033119-95458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033121-71362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033121-84376.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033121-67775.png)
故当n=1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033119-71125.png)
点评:在求数列的通项公式时,常用的一种方法是构造新数列,通过构造的新数列是等差数列或等比数列来求。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033045-55499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033045-86473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033045-17925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033045-52962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033005-67727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033005-39931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033006-27706.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033005-67727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033006-81172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033006-37148.png)
(3)令
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033006-11005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033007-79518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033007-23671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010033007-13232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032940-92494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032940-20985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032940-47663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032941-76560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032941-49917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032941-42341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032942-36370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032942-17931.png)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032941-42341.png)
(2) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032940-92494.png)
(3) 若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032942-45827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032941-42341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032942-67626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032942-62236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032943-83386.png)
.求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032943-52931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032943-83386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032802-97577.png)
(2)试用数学归纳法证明:对于n∈N*,点Pn都在(1)中的直线l上.
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032741-43897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032741-79938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032741-51930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032742-88080.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032741-43897.png)
(2)记
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032742-49585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010032741-79938.png)
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