名校
解题方法
1 . 若无穷数列{
}满足如下两个条件,则称{
}为无界数列:
①
(n=1,2,3......)
②对任意的正数
,都存在正整数N,使得n>N,都有
.
(1)若
,
(n=1,2,3......),判断数列{
},{
}是否是无界数列;
(2)若
,是否存在正整数k,使得对于一切
,都有
成立?若存在,求出k的范围;若不存在说明理由;
(3)若数列{
}是单调递增的无界数列,求证:存在正整数m,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
②对任意的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700458c01a7ad031e27d80ed43e9e882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a701eb81a1e88c69357f9eae5915ee.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff1c33b81ac2f065d37faef37504bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee912af5e2313d631ff3016ca7cc32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff1c33b81ac2f065d37faef37504bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fef5f2a4235817fb704d29e08766e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bec3181d9f88a68fb7470d0c9beb183.png)
(3)若数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7407503edea1b02e3084387c8a328d9e.png)
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2022-03-31更新
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8卷引用:北京市房山区2022届高三一模数学试题
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