名校
1 . 设
,若无穷数列
满足以下性质,则称
为
数列:①
,(
且
).②
的最大值为k.
(1)若数列
为公比为q的等比数列,求q的取值范围,使得
为
数列.
(2)若
数列
满足:
,使得
成等差数列,
①数列
是否可能为等比数列?并说明理由;
②记数列
满足
,数列
满足
,且
,判断
与
的单调性,并求出
时,n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94555857a26590865f337f8c4a93c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bcb79f2d16d369d4a6e32da7eca6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a0380833a2210fe0a279413e70eedb.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94555857a26590865f337f8c4a93c37.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94555857a26590865f337f8c4a93c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d33296d69857230998bd8152f2457d1.png)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4188680e5320653753ad0340439cb77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da321100bc025f1099f6a544ad0850a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ade3a1d01605706801e238726e55fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86dcea6d6efedf628ada9322f13590a.png)
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4卷引用:第4章 数列(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(苏教版2019选择性必修第一册)
第4章 数列(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(苏教版2019选择性必修第一册)(已下线)第4章 数列 单元综合检测-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)第4章 数列 单元综合检测(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)江苏省盐城中学2022届高三下学期5月仿真模拟数学试题
名校
解题方法
2 . 对于数列
,若从第二项起,每一项与它的前一项之差都大于或等于(小于或等于)同一个常数d,则
叫做类等差数列,
叫做类等差数列的首项,d叫做类等差数列的类公差.
(1)若类等差数列
满足
,请类比等差数列的通项公式,写出数列
的通项不等式(不必证明);
(2)若数列
中,
,
.
①判断数列
是否为类等差数列,若是,请证明,若不是,请说明理由;
②记数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
(1)若类等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8b1261de54b824c12b6887053416c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0566ce71a91f5939b92eb8d59e8ec5.png)
①判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
②记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c806dc9bf2cad0cb20220d23bd252a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29858a858c8ec1e1c65db718400a4a95.png)
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|
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6卷引用:4.2.3 等差数列的前n项和-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)
(已下线)4.2.3 等差数列的前n项和-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)4.2.2.1 等差数列的前n项和公式(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)(已下线)4.1 等差数列(第2课时)(十三大题型)(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)专题03 等差数列(二十三大题型+过关检测专训)(4)四川省成都市双流区2021-2022学年高一下学期期末数学试题上海市七宝中学2023届高三下学期开学考试数学试题
名校
3 . 定义首项为1且公比为正数的等比数列为“M-数列”.
(1)已知等比数列{an}满足:
,求证:数列{an}为“M-数列”;
(2)已知数列{bn}满足:
,其中Sn为数列{bn}的前n项和.
①求数列{bn}的通项公式;
②设m为正整数,若存在“M-数列”
,对任意正整数k,当
时,都有
成立,求m的最大值.
(1)已知等比数列{an}满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6355147af3dc3a7ed7457ebec2609426.png)
(2)已知数列{bn}满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94b69ac2e58e469427775f19ad1dd40.png)
①求数列{bn}的通项公式;
②设m为正整数,若存在“M-数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3d686e972baa72df81389555897acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41075383e3b80a1ac8faf5edec08f620.png)
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2卷引用:重庆市南开中学校2021-2022学年高二下学期5月月考数学试题
名校
4 . 已知{
}是公差不为0的无穷等差数列.若对于{
}中任意两项
,
,在{
}中都存在一项
,使得
,则称数列{
}具有性质P.
(1)已知
,判断数列{
},{
}是否具有性质P;
(2)若数列{
}具有性质P,证明:{
}的各项均为整数;
(3)若
,求具有性质P的数列{
}的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4877a6af6f2064a3ba51773238144038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27e98494d259c776f02d40202386909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)若数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cceacfd0395da804e9fd4878fbd93080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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|
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9卷引用:北京市西城区2021-2022学年高二下学期期末考试数学试题
北京市西城区2021-2022学年高二下学期期末考试数学试题(已下线)4.2.1-4.2.2 等差数列的概念和通项公式-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)4.2.1等差数列的概念(第1课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)北京市海淀区中央民族大学附属中学2022-2023学年高二下学期期中考试数学试题(已下线)4.1 等差数列(第1课时)(十大题型)(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)模块三 专题2 新定义专练【高二下人教B版】北京市第六十六中学2023-2024学年高二下学期4月期中质量检测数学试题(已下线)北京市第四中学2023-2024学年高三下学期开学测试数学试卷(已下线)2024年新课标全国Ⅰ卷数学真题变式题16-19
名校
解题方法
5 . 若数列
中存在三项,按一定次序排列构成等比数列,则称
为“
数列”.
(1)分别判断数列1,2,3,4,与数列2,6,8,12是否为“
数列”,并说明理由;
(2)已知数列
的通项公式为
,判断
是否为“
数列”,并说明理由;
(3)已知数列
为等差数列,且
,求证
为“
数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff35e4e3cdc188643c46265591575c6.png)
(1)分别判断数列1,2,3,4,与数列2,6,8,12是否为“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff35e4e3cdc188643c46265591575c6.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffbf1bc31b86e9ee9f83a129374d663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff35e4e3cdc188643c46265591575c6.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599f868b1c8a83d7227f5e6a793044cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec4b4a628ce4482e16a3edc2953fc8.png)
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3卷引用:北京市房山区2021-2022学年高二下学期期末检测数学试题
北京市房山区2021-2022学年高二下学期期末检测数学试题(已下线)4.3.1 等比数列的概念(第2课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)北京市顺义区第一中学2022-2023学年高二下学期6月月考数学试题
6 . 已知
为正整数,数列
:
,记
.对于数列
,总有
,
,则称数列
为
项0-1数列.若数列A:
,
:
,均为
项0-1数列,定义数列
:
,其中
,
.
(1)已知数列A:1,0,1,
:0,1,1,直接写出
和
的值;
(2)若数列A,
均为
项0-1数列,证明:
;
(3)对于任意给定的正整数
,是否存在
项0-1数列A,
,
,使得
,并说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83590c4a7ea5636843dd4b60c67cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6eebdcb5458e76931806d7d001e7d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a492010ae000022884ff8648ab95215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c365eeee68c896623c8a9f4d1a4e0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d64beb75ea4cfc016995a81de4160e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5231cb0bfedf2f963c1830adfd74aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a37472927e5adf5d10ea71516ffdcd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30a09719b90ab0a9344522451d754b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c365eeee68c896623c8a9f4d1a4e0f7.png)
(1)已知数列A:1,0,1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2952a31b68a2bb188ad215e109e7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc53bf6c5c8ac960186362af2158994f.png)
(2)若数列A,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6025c89963745b2f6bb2c45b4e03b225.png)
(3)对于任意给定的正整数
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d3076f01e163e656818cd4999f00ce.png)
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|
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6卷引用:北京市海淀区2021-2022学年高二下学期学业水平调研数学试题
北京市海淀区2021-2022学年高二下学期学业水平调研数学试题北京市广渠门中学2022-2023学年高二下学期第一次月考数学试题北京市顺义牛栏山第一中学2022-2023学年高二下学期期末数学复习试题(一)【北京专用】专题03数列(第三部分)-高二上学期名校期末好题汇编(已下线)专题01 数列(6大考点经典基础练+优选提升练)-【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(新高考专用)北京市昌平区第一中学2024届高三上学期期中考试数学试题
解题方法
7 . 已知数列
是无穷数列.若
,则称
为数列
的1阶差数列;若
,则称数列
为数列
的2阶差数列;以此类推,可得出数列
的
阶差数列,其中
.
(1)若数列
的通项公式为
,求数列
的2阶差数列的通项公式;
(2)若数列
的首项为1,其一阶差数列
的通项公式为
,求数列
的通项公式;
(3)若数列
的通项公式为
,写出数列
的
阶差数列的通项公式,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703cdc7668aa4dcab77e448249f9446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28182f211c5a2647e5963f94b7e39615.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dd3ce757a2ad080ece0e34424fb05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fef6975d285cabcf6be67c78f30d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7614e7ffdeb8b48c6aaf660c4fef3e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
8 . 对给定实数p,若数列
满足以下三个条件:①
,
;②对任意正整数n,
;③对任意正整数m、n,
.则称数列
为“
数列”.
(1)对前4项为2、
、0、2的数列,可以是
数列吗?说明理由;
(2)若
是
数列,求
的值;
(3)是否存在常数p,使得存在
数列
,对任意正整数n,均满足
?若存在,求出所有这样的p;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745d0ee776d181c17e47a02ccb15d964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaadbdd9c681dc356df6e818715734c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d5f516c361e9e473f80029ef87c790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2339f8358985e5c65bd6cc40cc46fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6a3d29b15d91f1a49ae0c4bbf78a77.png)
(1)对前4项为2、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b628d87cb667a0a31766a88c6c426324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(3)是否存在常数p,使得存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6a3d29b15d91f1a49ae0c4bbf78a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1391b1323ca839ae8bcc075f9387935f.png)
您最近一年使用:0次
名校
9 . 已知数列
. 若存在
,使得
为递减数列,则
称为“
型数列”.
(1)是否存在
使得有穷数列
为
型数列?若是,写出
的一个值;否则,说明理由;
(2)已知2022项的数列
中,
(
). 求使得
为
型数列的实数
的取值范围;
(3)已知存在唯一的
,使得无穷数列
是
型数列. 证明:存在递增的无穷正整数列
,使得
为递增数列,
为递减数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30f366b7d87e5e748367ac0a9df554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ad05e306652c42534c41636f5942ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30f366b7d87e5e748367ac0a9df554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fb9c93285f73ce392c6b8d3b2a8f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知2022项的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a55e4115c36490a40f83d15f066bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e306979e87a3cd19b2f390d374956f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a401c6c57a4aa884504b7a20a75b026a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a55e4115c36490a40f83d15f066bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)已知存在唯一的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30f366b7d87e5e748367ac0a9df554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bdb46e94cc0d92ebb508eec108ba531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbcb218505bec13380c6a2d730dd39c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d0ec71294e306ec78aac52f6753174.png)
您最近一年使用:0次
2022-06-23更新
|
587次组卷
|
4卷引用:专题06数列必考题型分类训练-3
10 . 若数列
同时满足下列两个条件,则称数列
具有“性质A”.
①
(
);②存在实数
,使得对任意
,有
成立.
(1)设
,试判断
是否具有“性质A”;
(2)设递增的等比数列
的前n项和为
,若
,证明:数列
具有“性质A”,并求出A的取值范围;
(3)设数列
的通项公式
,若数列
具有“性质A”,其满足条件的A的最大值
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e772be971634dc7230df59d91399dc59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670d5fc71b49fdb5411b046bb9a81bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c46b33730f3a29b9ec3024df71375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b39b97c1f6007e458646cf2655a0974.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a234044b6e65e53f5f0d979886be4f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942ed174dfdafaf5f0a68cac579110f8.png)
(2)设递增的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe308769d98da3757d3d3c9019ea84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325bb1f4a88ca4e5bed08b5a4ede97ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f27f0c9be9710c55ab8e8d2cb4e56df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-06-23更新
|
623次组卷
|
4卷引用:专题06数列必考题型分类训练-3