名校
解题方法
1 . 已知各项均为正数的数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dfc7deedbce96f57f713356c9fd1b.png)
.
(1)求证:数列
是等差数列,并求
的通项公式;
(2)若
表示不超过
的最大整数,如
,求
的值;
(3)设
,
,问是否存在正整数m,使得对任意正整数n均有
恒成立?若存在求出m的最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dfc7deedbce96f57f713356c9fd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd6d0291f5e8c4bc9ff01ebd7c2ceda.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d1e3a06f59a35396aac6e12c5e2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8127107063b06516e240d2e38eb8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14ba2d83196ac59b817280f01ed150b.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecfecaf98016d5209a0ee37fa34a876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b519f2287a07079f6ca20588d06171f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e252b80bd7ce02505ca9745fe8e2d15.png)
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2022-07-21更新
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861次组卷
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3卷引用:四川省遂宁市遂宁中学校2021-2022学年高一下学期期末数学试题