题目
题型:不详难度:来源:
设各项均为正数的数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104528-72761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104528-95136.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-27114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-22560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-51649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-51649.gif)
数列.
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104528-72761.gif)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-57016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-11235.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-29226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-43551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-21796.gif)
求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-50318.gif)
答案
(本小题主要考查数列、不等式等知识, 考查化归与转化、分类与整合的数学思想方法,以及抽象概括能力、推理论证能力、运算求解能力和创新意识)
(1)解:∵数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-22560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-51649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-51649.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104531-84071.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104531-65387.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104531-25205.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104531-41933.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104532-31035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104532-54787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104532-49103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104533-12796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104533-63302.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104533-59229.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104533-72895.gif)
(2)解:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-57016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104534-32139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104534-14198.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104534-83507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104534-52288.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-11235.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104535-63947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104535-23306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104535-72666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104535-21312.gif)
故要使不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104529-11235.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-29226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-43551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-21796.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104536-90409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-29226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-43551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-21796.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104536-45428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-43551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-21796.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104536-16449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104536-17524.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-57989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-58098.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-64540.gif)
∴实数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-50318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-59225.gif)
[另法]:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104538-77325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104538-98092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104538-71021.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-57989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-58098.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-64540.gif)
∴实数
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104530-50318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104537-59225.gif)
解析
核心考点
试题【(本小题满分14分)设各项均为正数的数列的前项和为,已知数列是首项为,公差为的等差数列.(1) 求数列的通项公式;(2)令,若不等式对任意N都成立,求实数的取值】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
已知等差数列{an}中a2=8,S10=185.
(1)求数列{an}的通项公式an;
(2)若从数列{an}中依次取出第2,4,8,…,2n,…项,按原来的顺
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104521-38487.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104521-72910.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104514-32282.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104514-17619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104515-14226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104515-79234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104515-58349.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104501-38079.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104501-54380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104502-58486.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104502-53398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104502-57913.gif)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104502-53317.gif)
(Ⅲ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104503-54807.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104503-88915.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104503-84259.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104448-90879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104448-99969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104449-24649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104432-43923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104433-15998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104433-38622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104433-88278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104433-85179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104434-95736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104434-20522.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104432-43923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104433-88278.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104434-36191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104434-28484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011104433-85179.png)
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