题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-47262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-93389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024754-93968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024754-81315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024754-90418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024754-40895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024754-93968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024754-55398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024755-78980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024755-78980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024755-82007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024755-23836.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024756-29907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024755-23836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
(2)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024756-33864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024756-75269.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-70040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-73278.png)
②记数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-19835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-92521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-73278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-54829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-73278.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-19788.png)
(2)①
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-73278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-90653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-15740.png)
解析
试题分析:(1)根据数列的定义求出当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024756-29907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-19835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-13841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-73278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-80037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-27200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024810-43422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024810-29933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024810-88448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-27200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024755-23836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-54829.png)
试题解析:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024810-11391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024811-28546.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024811-38133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024811-20289.png)
故数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024753-18898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-19788.png)
(2)①因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024811-65809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-13841.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024811-31523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-13841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024812-14257.png)
则数列的一个周期至少有
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024812-47124.png)
所以第
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024812-21941.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024812-45153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024813-92522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024813-90921.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024813-27161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024813-16359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024813-20828.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-73278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-90653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-15740.png)
②因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024814-51025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024814-81628.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024814-80869.png)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024810-43422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024814-24303.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024755-82007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024815-91464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024815-73391.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024815-69132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024810-88448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024815-11252.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024809-27200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024815-64044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-54829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024807-73278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024808-19835.png)
核心考点
试题【已知无穷数列中,、 、、构成首项为2,公差为-2的等差数列,、、、,构成首项为,公比为的等比数列,其中,.(1)当,,时,求数列的通项公式;(2)若对任意的,都】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)若数列{bn}满足
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024731-73595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024731-44964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024732-97323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024732-40025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024713-80114.png)
(Ⅰ)当a1=19时,a2014= ;
(Ⅱ)若an是不为1的奇数,且an为常数,则an= .
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)证明:对一切正整数n,有
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024703-21731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024704-54523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024704-26948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024704-55634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024634-61455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024634-46913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024635-57286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024635-55285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024635-45378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024635-14190.png)
(Ⅱ)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024636-34052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024636-19515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024635-55285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024636-60353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024618-23124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024618-12764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024619-89554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024619-46865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012024619-52973.png)
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