题目
题型:不详难度:来源:
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080545-36027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080546-56440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080546-11546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080546-95904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080546-30455.png)
(Ⅰ)证明数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080547-38347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080545-36027.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080547-59653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080547-42490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080546-56440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080547-93998.png)
(Ⅲ)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080545-36027.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080548-75371.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080548-97565.png)
(Ⅲ)不存在满足条件的三项.
解析
(1)把Sn和Sn+1相减整理求得an+1=2an+3,整理出3+an+1=2(3+an),判断出数列{3+an}是首相为6,公比为2的等比数列,求得3+an,则an的表达式可得.
(2)把(I)中的an代入bn,求得其通项公式,进而利用错位相减法求得数列的前n项的和.
(3)设存在满足题意,那么等式两边的奇数和偶数来分析不存在。
解析:(Ⅰ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080546-95904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080548-86070.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080549-36160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080549-69264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080549-75542.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080547-38347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080549-40444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080549-50213.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080548-75371.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080550-48967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080550-52856.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080550-33019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080550-75003.png)
①-②得,
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080550-27796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080551-93868.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080548-97565.png)
(Ⅲ)设存在
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080551-98817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080551-16107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080551-19021.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080557-86708.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080557-72163.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080558-34114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080558-61956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080558-53518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080558-60141.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080558-34114.png)
核心考点
试题【(本题满分12分)已知数列的前项和为,().(Ⅰ)证明数列是等比数列,求出数列的通项公式;(Ⅱ)设,求数列的前项和;(Ⅲ)数列中是否存在三项,它们可以构成等差数】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080516-90131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080516-17468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080516-38665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080516-37834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080517-76683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080517-65345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080517-46661.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080516-90131.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080516-90131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080517-34876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080518-70510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080518-42244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080518-81591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080517-46661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080518-56577.png)
(3)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080519-91557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080519-76595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080507-67667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080507-70121.png)
A.16 | B.17 | C.18 | D.19 |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080414-82061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080414-89531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080414-77767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080414-46124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080415-63645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080407-78732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080407-40529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080407-36383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080354-47851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080354-51387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080354-96130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080354-77766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080355-15794.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080355-89778.png)
(2)试写出一个区间
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080355-42677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080355-80671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080354-77766.png)
(3)若已知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080356-67535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010080356-82922.png)
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