1 . 黎曼猜想由数学家波恩哈德∙黎曼于1859年提出,是至今仍未解决的世界难题.黎曼猜想研究的是无穷级数
,我们经常从无穷级数的部分和
入手.请你回答以下问题:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1e7df075a8aea5c473b84fbe93b4a6.png)
_____ ;(其中
表示不超过
的最大整数,如
)
(2)已知正项数列
的前
项和为
,且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96c7a4f80a6323ab9957d1fabe391fc.png)
_________ .(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc07ef1256a9188949462dff0bc9be7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b3bd282c6e7cad9cf53cde43b122da.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1e7df075a8aea5c473b84fbe93b4a6.png)
![](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/40ca5bb1a4a8e02c13874056ccdeb27e.png)
(2)已知正项数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9583a4d9bf7b954042226232d23a8c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96c7a4f80a6323ab9957d1fabe391fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227cad9f324ed0089526402e3977f329.png)
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名校
2 . 在处理多元不等式的最值时,我们常用构造切线的方法来求解.例如:曲线
在
处的切线方程为
,且
,若已知
,则
,当
时等号成立,所以
的最小值为3.已知函数
,若数列
满足
,且
,则数列
的前10项和的最大值为________ ;若数列
满足
,且
,则数列
的前100项和的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c72a671c1fba30deaf0f1bbbd4f34df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7152aea5d046953a8c931571be7c529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb815fd4ab37e3acce07473dddc6d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f285defc2f91858fae9472d090ef34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4dd6e208196f02dba2106dbcfb68569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8285778d6832045498a16d1ceb1da957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91540ab4e6e0ac4b7be750ad9f9c5f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a871d59989f13df946a72de050e7ec53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f79a1c4c9f83d94fe1ebcc3ecfc0a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065054f4e163585d630aa42cb6323a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36562bec957b5ab3ca3b64bc3dc1c1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282328f6df9c9c524084dc76f8499a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a083c38783fda991b05eaf051ee6c1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a4465705237c08e4e05d849cb28d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/792ce88874b917946843d4ed3da3ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b7ab69e9605abf49d8d42c2382bb24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed63f4ab8e272b2b0083b2086315e1b1.png)
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2022-10-20更新
|
323次组卷
|
2卷引用:广东省广州市华南师范大学附属中学2023届高三上学期第一次月考数学试题
名校
解题方法
3 . 黎曼猜想由数学家波恩哈德·黎曼于1859年提出,是至今仍未解决的世界难题.黎曼猜想研究的是无穷级数
,我们经常从无穷级数的部分和
入手.已知正项数列
的前
项和为
,且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242e664612a1258c9087a68bf449ffa5.png)
______ .(其中
表示不超过
的最大整数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc0aef4bfbe8f19dc851f7512985088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae3f43e195025f1d86d1f5f5e80aa61.png)
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9583a4d9bf7b954042226232d23a8c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242e664612a1258c9087a68bf449ffa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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4 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedd7be672b179eaf072f53635fe130b.png)
_____ ;若直线
(
)与函数
的图象有交点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd0690b529099376398a467c9c0612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedd7be672b179eaf072f53635fe130b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd0690b529099376398a467c9c0612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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