1 . 已知数列
的前n项和为
,且满足
,
.
(1)判断
是否为等差数列?并证明你的结论;
(2)求
和
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a022b4111eeada0a90412ab74e2ad325.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31066efaa85cde2cedf2cb065bbc162a.png)
您最近一年使用:0次
2024-01-11更新
|
1627次组卷
|
4卷引用:上海市青浦高级中学2023-2024学年高二上学期期末考试数学试题
上海市青浦高级中学2023-2024学年高二上学期期末考试数学试题(已下线)每日一题 第26题 由Sn求an 作差检验(高二)河南省南阳市第一中学校2023-2024学年高二下学期第一次月考数学试题(已下线)模块六 大招4 数列不等式的放缩
2 . 已知
,数列
为
,规律是在
和
中间插入
项,所有插入的项构成以3为首项,2为公差的等差数列
,则数列
的前30项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aac186947a2ee83597d9949143fd1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2024-01-02更新
|
772次组卷
|
6卷引用:4.2 等比数列(第2课时)(六大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)4.2 等比数列(第2课时)(六大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(七)江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(三)(已下线)考点7 等差、等比数列的联姻 2024届高考数学考点总动员(已下线)高三数学开学摸底考02(新考法,新高考七省地区专用)(已下线)压轴题05数列压轴题15题型汇总-1
2024·全国·模拟预测
3 . 已知数列
满足
,若
对
恒成立,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a9d26c7081258cd815a19c642da1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
4 . 已知直线
与
相交于点
,直线
与
轴交于点
,过点
作
轴的垂线交直线
于点
,过点
作
轴的垂线交直线
于点
,过点
作
轴的垂线交直线
于点
,
,这样一直作下去,可得到一系列点
,
,
,
,
,记点
的横坐标构成数列
,给出下列四个结论:
①点
; ②数列
单调递增;
③数列
为等比数列; ④
.
其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d75e9b0329424f08758cd86fe72dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb9b8e2ff79c75a12c73cf474df5f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3300966c23d3c62e0c30327faf8163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fe66db7cd1a603298df7c219431957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d497e59ca415b9973ae8b07cd28e472.png)
③数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fa575eec471d20667624bd4e9f7924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b16a1cacd1be1014c6acb0267c0715.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
解题方法
5 . 数列
满足
,其中
为数列
的前
项和.
(1)判断数列
是否是等比数列,并说明理由;
(2)若
为数列
的前
项和,求
与
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18b4f2f085b8e32b92862fdd42d5b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa97c7ae99ad7a17417f75ea514afd6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1f2554444735b544debcd68f4cb28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13aababf2d1ee2f7c5336857f0fcb7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
6 . 已知数列
满足
,且对任意正整数
,关于
的实系数方程
都有两个相等的实根.若
,则满足条件的不同实数
的个数为____________ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fca8d37353fb72382ec09fd6db54ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebf3af4320e037b6fd9938d6e70d534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-12-18更新
|
256次组卷
|
3卷引用:期末测试卷02(测试范围:第1-8章+集合+不等式+函数)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
(已下线)期末测试卷02(测试范围:第1-8章+集合+不等式+函数)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)(已下线)专题01 数列(九大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)上海市浦东新区2024届高三上学期期末教学质量检测数学试题
解题方法
7 . 已知平面上有
个点
,
,
,
,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bdda8ec472fb7f07c7213bf6f063b1.png)
且
,记
的坐标为
,将
,
,
依次顺时针排列,求
=________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039af66355ed85ff4c204931b882b694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c97d15ede1ffecd6035c4e196e557f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f18f1cec532d6835b69b99704df0d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688d97dccaf3c1259e2f1f8fd525bedc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bdda8ec472fb7f07c7213bf6f063b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd43fd553146f09a4381dcdbf0458cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceec3ca529adb8c49f9e3db40256e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2b289b20ecde54bf91c3a0bd5869e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039af66355ed85ff4c204931b882b694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c97d15ede1ffecd6035c4e196e557f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85462bd19666677a46625c60deadd979.png)
您最近一年使用:0次
2023-12-16更新
|
301次组卷
|
5卷引用:第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)上海市嘉定区2024届高三上学期质量调研数学试题上海市普陀区长征中学2024届高三上学期10月月考数学试题(已下线)第16题 数列递推求通项(高三二轮每日一题)
名校
解题方法
8 . 设数列
的前n项和为
,对一切
,点
都在函数
图象上.
(1)求
,归纳数列
的通项公式(不必证明);
(2)将数列
依次按1项、2项、3项、4项循环地分为
、
、
、
、
、
、
、
、
、…,分别计算各个括号内各数之和,设由这些和按原来括号的前后顺序构成新的数列为
,求
的值;
(3)设
为数列
的前n项积,若不等式
对一切
都成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cff7a7deafe061d63e324c12867f958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e6e0e0522300b27c59ea1920a7b725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc15b8864ee2c70e75b70684b7a2b5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)将数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b216d768026fa703c4a84ae2a8df0449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f083a6f04943110c24d0add2757bc501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8fe375194804d7482ff4403790d6a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc03993fe8538b814101c933896c5e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0449a2f9b428ce24935c4b11d1b71a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd71c79c25de550c3a1d84e65c18f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c4f28ba6dfb178034ed7eded576f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fe365cd7f9f94dcbd53750639530e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151f4f1a38fa5f79551b1d9c5d228e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cf41b06e34f87048496c44e744acac.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09953c3d3c8bb8566bb740c3a7d53e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5fbb470763c84103da1ed280e35d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
您最近一年使用:0次
名校
解题方法
9 . 关于曲线
,有下述两个结论:①曲线
上的点到坐标原点的距离最小值是
;②曲线
与坐标轴围成的图形的面积不大于
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93235b3c3c78325c8b58d4bb9bf9b2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
A.①、②都正确 | B.①正确 ②错误 | C.①错误 ②正确 | D.①、②都错误 |
您最近一年使用:0次
2023-12-06更新
|
279次组卷
|
5卷引用:上海市通河中学2023-2024学年高二上学期期末考试数学试题
上海市通河中学2023-2024学年高二上学期期末考试数学试题上海市青浦区朱家角中学2023-2024学年高二上学期期末考试数学试题(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)上海市松江区2024届高三上学期期末质量监控数学试题(已下线)期末真题必刷压轴60题(23个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
解题方法
10 . 已知
为不超过
的最大整数,例如
,
,
,设等差数列
的前
项和为
且
,记
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4卷引用:第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)广东省广州市天省实验学校2023—2024学年高二上学期12月月考数学试题江苏省淮安市淮阴中学、姜堰中学等三校2024届高三上学期12月阶段性测试数学试题(已下线)【练】专题4 数列新定义问题