1 . 已知数列
是无穷数列,满足
.
(1)若
,
,求
,
,
的值;
(2)求证:“数列
中存在
使得
”是“数列
中有无数多项是1”的充要条件;
(3)求证:存在正整数k,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5bad0e0832bbf42a12f4efc86cfe0e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(2)求证:“数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fb67a858cf21e675a4be5ae0bc49c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b64e4722de7deb7c05ca986166e6eb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求证:存在正整数k,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bded46375833efe7c9143aa80f8d64.png)
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2020-09-13更新
|
1024次组卷
|
3卷引用:上海市复旦大学附属中学青浦分校2020届高三下学期开学摸底数学试题
上海市复旦大学附属中学青浦分校2020届高三下学期开学摸底数学试题2020届北京市中国人民大学附属中学高三上学期期中模拟统练(七)数学试题(已下线)专题15 数列不等式的证明 微点6 数列不等式的证明综合训练
名校
2 . 已知集合
并且
.定义
(例如:
).
(1)若
,
,集合A的子集N满足:
,且
,求出一个符合条件的N;
(2)已知集合
满足:
,
,其中
为给定的常数,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a7021c45e2fed11d8b3079477d056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90edcabb371b5698ed97986bdacc798d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66013cb08f923b6c0ae943aa017d3647.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c0131e62f174b8eb65a1c20095390c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522954ce536d559cf03638d87fad504c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3b83ccd27fced5b6f12d4737d0f92a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578632629c97349c61efb26c6acda273.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8cfe3398b682019dbe75b160ec8411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1e869016b45f1560da47ba9dbe7ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6b17f4e51916675e797cc9b2e95346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40451e0f90ba4df0cb35143b93303a22.png)
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