题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042414-71208.png)
(1)判断数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042414-27148.png)
(2)求an;
(3)当a=1时,令bn=
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042414-53260.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042414-15071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042415-14419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042415-99882.png)
解析
试题分析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042415-65759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042415-70844.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042415-61322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042416-29838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042416-99552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042416-41806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042416-97557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-87374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-89587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-68130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042414-15071.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042416-41806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-92940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-70206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042418-16832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-68130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042418-43188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042418-23928.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042418-63330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042418-45164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042419-39995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042416-41806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042419-65615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042415-14419.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042419-97693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-68130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042419-99071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042420-15542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042420-19045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042420-64151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042417-68130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042420-51693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042421-80254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042421-81300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042421-94954.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042421-85325.png)
而当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042422-85719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042422-94836.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042422-51085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042422-56564.png)
综上所述,
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042422-56159.png)
点评:(1)本题主要考查了等比数列的通项公式、等比数列求和公式、简单递推数列求通项、错位求和等知识,考查了学生的运算能力,以及化归与转化、分类讨论的思想.(2)利用错位相减法求和时,转化为等比数列求和,若公比是个参数(字母),则应先对参数加以讨论,一般情况下,分为等于1和不等于1两种情况分别求和。
核心考点
试题【已知数列{an}满足:a1=1,a2=(a≠0),an+2=p·(其中P为非零常数,n∈N *)(1)判断数列{}是不是等比数列?(2)求an;(3)当a=1时】;主要考察你对数列综合等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042403-91271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042403-51837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042403-66533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042403-24662.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042403-91271.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042404-60178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042404-67117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042403-51837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042404-57398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042404-94883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042356-39419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042356-25273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042356-17077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042356-58976.png)
(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042357-46778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042357-62127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042350-64016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042351-58972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042351-90451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042341-69505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042342-33708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042342-22639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042342-83509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042342-50294.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042341-69505.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042343-86566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042343-21243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042342-22639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042343-52641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042336-78868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042336-83139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042337-24098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042336-78868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015042337-32064.png)
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