1 . 若有穷数列
(
是正整数),满足
(
,且
,就称该数列为“
数列”.
(1)已知数列
是项数为7的
数列,且
成等比数列,
,试写出
的每一项;
(2)已知
是项数为
的
数列,且
构成首项为100,公差为
的等差数列,数列
的前
项和为
,则当
为何值时,
取到最大值?最大值为多少?
(3)对于给定的正整数
,试写出所有项数不超过
的
数列,使得
成为数列中的连续项;当
时,试求这些
数列的前2024项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22fc26a14e8e5987688565881fb71e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61fbe58f038432c468241d2771fb85d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e4bf506906957dc3bceb5fd3718514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447e5baee4f7518706498d4aca7553b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfab6833cbc260b8482f13de6b05f35d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d734d660b7e9d5992ac95f31f9d9217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54f81fd86f64a74ef363086ada77d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394aee19f94c2b70fcce1d69b31dc7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342d9276c99f962d3045ee8dab5a2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342d9276c99f962d3045ee8dab5a2d5.png)
(3)对于给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6315a20e3ecd1768ae381e2a87610bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f5bcbc1c51b653b25bc1e76763036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addee6ce5163a2580888ce2da22714af.png)
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|
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2卷引用:海南省琼海市嘉积中学2023-2024学年高三下学期一模考试数学试题
名校
解题方法
2 . “0,1数列”在通信技术中有着重要应用,它是指各项的值都等于0或1的数列.设A是一个有限“0,1数列”,
表示把
中每个0都变为1,0,每个1都变为0,1,所得到的新的“0,1数列”,例如
,则
.设
是一个有限“0,1数列”,定义
,
、2、3、
.则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e3d87be9f706832ef25537d78a201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edc631d8880daae668cef7c72790ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5a03f4d0258927e2815b75301274c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f939918bc9c36dbb32e8e1d7853b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
A.若![]() ![]() |
B.对任意有限“0,1数列”![]() ![]() |
C.![]() ![]() |
D.若![]() ![]() ![]() |
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2卷引用:海南省琼海市嘉积中学2022届高三下学期第一次月考数学试题
名校
3 . 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)
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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