1 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f328740bf24bfa5307d5ba23cfaac1.png)
(2)已知
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f328740bf24bfa5307d5ba23cfaac1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d227c4e80e72eb343659193a06daff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e28564e8971ee3cd8deb50d1afab24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629abc79d5be8093ee40ef9f6eb19337.png)
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名校
2 . (1)计算:
.
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019ed2ce5ab9e901853c4e7d6985e4b5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f8f684537b46195dde4f8f48579fcb.png)
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名校
解题方法
3 . 化简
(1)
;
(2)已知
是第三象限角,化简
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd0a43a89dffefe41bf10c81d6fdf0c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e61123c3d2642a2de5582967f581df.png)
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解题方法
4 . 已知
,计算
(1)
;
(2)
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff8e8f399db20c51e878b2b4b134793.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08a1ffade82fb4a26656af64da60ca5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617e59c1afb7dc761f5b373bc820ecff.png)
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解题方法
5 . 化简:
(1)
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c71c7211485d14dd662733b2c010d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb312c14dbe3ccf95649b29a2c1f3b5b.png)
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6 . 求最大的实数
,使得对任意的正整数
和
个实数
,
,
,
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9401b82f59e0b3dc2bc1bda73804d068.png)
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2023-12-15更新
|
124次组卷
|
2卷引用:2023年第39届全国中学生冬令营(CMO)数学试题
7 . 已知数列
满足:
.
(1)求
的通项公式;
(2)记
,
(i)求
的值;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed584207d8b1308d4c4634c6d07bde15.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2ea025449d8d7d4a8d22dfb1ff5425.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a323ef99ce96bef2781553fdc1c724e.png)
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