名校
1 . 已知
,等差数列
的前
项和为
,记
.
(1)求证:函数
的图像关于点
中心对称;
(2)若
、
、
是某三角形的三个内角,求
的取值范围;
(3)若
,求证:
.反之是否成立?并请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71de2abab31c4eb56f306f90dab97b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/5395b2d08fce7c50d6281ef406cfe4bf.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd4b78b52a322453c700b62660e6ca57.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c5f3a5c55e0c95191c5a893f63062.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4847cf7c0d99d9c83ca571bef8eefc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58b9a59084755c0a4781922cfa03ee5.png)
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2023-04-13更新
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1039次组卷
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3卷引用:专题06 数列及其应用