名校
1 . 对于数列
,称
(其中
)为数列
的前k项“波动均值”.若对任意的
,都有
,则称数列
为“趋稳数列”.
(1)若数列1,
,2为“趋稳数列”,求
的取值范围;
(2)已知等差数列
的公差为
,且
,其前
项和记为
,试计算:
(
);
(3)若各项均为正数的等比数列
的公比
,求证:
是“趋稳数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98816fb04cd9855c376352b915c41b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6aaee5e84eb6c6a4f339fe82c20025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6aaee5e84eb6c6a4f339fe82c20025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca48e93a553f5828b86e09f4d5f1042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(1)若数列1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370c1c8c958a7010fa144eb32e23f8d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f0bf06a83e595c7195e5c3cfd53a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea88016f672b8f54901e457cceecca1.png)
(3)若各项均为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecd48d65ac4f8197c45231f68e8bce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
您最近一年使用:0次
2020-02-01更新
|
1848次组卷
|
5卷引用:海南省琼海市嘉积中学2023-2024学年高三下学期高中教学第三次大课堂练习数学试题