23-24高二上·上海·期末
名校
1 . 定义:对于任意大于零的自然数n,满足条件
且
(M是与n无关的常数)的无穷数列
称为M数列.
(1)若等差数列
的前n项和为
,且
,
,判断数列
是否是M数列,并说明理由;
(2)若各项为正数的等比数列
的前n项和为
,且
,证明:数列
是M数列;
(3)设数列
是各项均为正整数的M数列,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f165a34038d89623948dbe0a669df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb8cf8df82fd05e5549ce9c1a6f3524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818548de2563bc81198611cf3468f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若各项为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c8a7aaf355cf3ea778c73eea8ae635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292852a3aa9790d661862ff0b67c8971.png)
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2024-01-14更新
|
1325次组卷
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8卷引用:湖北省荆州市沙市中学2023-2024学年高二下学期3月月考数学试题
湖北省荆州市沙市中学2023-2024学年高二下学期3月月考数学试题(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)安徽省六安第二中学2023-2024学年高二上学期期末统考数学试卷广东2024届高三数学新改革适应性训练三(九省联考题型)(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)模块五 专题5 全真拔高模拟5(北师大高二期中)(已下线)模块三专题2 数列的综合问题 【高二下人教B版】(已下线)模块三 专题4 数列的综合问题 【高二下北师大版】
名校
2 . 若有限项数列
满足
,则称数列
为
数列.记
.
(1)写出两个满足
,
的
数列
;
(2)若
,
,求证:
数列
是递增数列的充要条件是
;
(3)对任意给定的整数
,是否存在
的
数列
,满足
?如果存在,写出一个满足条件的
数列
;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ace20898425f9535833f48338a35d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992c86a01c5ba8d269c6809d89f2a120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b698319c8631e8c9793b4955f1c8a7.png)
(1)写出两个满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2750dc9a0ad9b327da7a92f524cb90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074da659cd80637181285e25ab5fba46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c7867969b14fd642147188b6ebf29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8243c5965a844b36d5fc5988b83362.png)
(3)对任意给定的整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac19e2a797cd0a408316988a63b3755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7e7148c3e777db25d6fa15d229bf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次
2021-11-27更新
|
164次组卷
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2卷引用:北京市顺义牛栏山第一中学2022届高三10月月考数学试题
解题方法
3 . 设数列
是等差数列,且公差为
,若数列
中任意不同的两项之和仍是该数列中的一项,则称该数列是“封闭数列”.
(1)若数列
中,
,
,求证:数列
是“封闭数列”;
(2)若
,试判断数列
是否为“封闭数列”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4ae73a6f9c290183bed81c5b622e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2021-09-22更新
|
400次组卷
|
5卷引用:福建省宁德市2022-2023学年高二上学期居家监测数学试题
福建省宁德市2022-2023学年高二上学期居家监测数学试题沪教版(上海) 高二第一学期 新高考辅导与训练 第7章 数列与数学归纳法 7.2(2)等差数列的定义与通项公式的应用人教A版(2019) 选修第二册 突围者 第四章 第二节 课时1 等差数列的概念沪教版(2020) 选修第一册 新课改一课一练 第4章 4.1.1 等差数列及其通项公式(已下线)4.1等差数列及其通项公式(第1课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件
4 . 已知有穷数列
.定义数列
的“伴生数列”
:
,其中
,规定![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14328f8e2f81d5ad6611b8ee13f04d67.png)
(1)写出下列数列的“伴生数列”:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c38f000c388fda76e180303fd1fa79.png)
(2)已知数列
的“伴生数列”
,且满足
.若数列
中存在相邻两项为
,求证:数列
中每一项均为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21cca25bc7b8cc4f79d853b3ea7a921a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7955afb1f12c680759d87880b2d4549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594efaf67d8487e3a437b70dacfac5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14328f8e2f81d5ad6611b8ee13f04d67.png)
(1)写出下列数列的“伴生数列”:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c38f000c388fda76e180303fd1fa79.png)
②
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be87a3508eaa7f2ffac1e1f34e66e21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3256704d8b25c2e0af3b734eb6f5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
2020-11-02更新
|
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|
3卷引用:北京科技大学附属中学2021届高三10月月考数学试题
5 . 如果数列
满足“对任意正整数
,都存在正整数k,使得
”,则称数列
具有“性质P”.已知数列
是无穷项的等差数列,公差为d
(1)若
,公差
,判断数列
是否具有“性质P”,并说明理由;
(2)若数列
具有“性质P”,求证;
且
;
(3)若数列
具有“性质P”,且存在正整数k,使得
,这样的数列共有多少个?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320e7710ac9aafc0ecaf91ba6686cea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab406d94b4907ab8a20ae3214628b045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f2572192cc7ca046e9a3155ef3e56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3068733ef2ceda9f1620d5c9bcdfa542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8e68eb4ade6e22982d2df5102d8894.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0af74258551ca3f28b2c6ce54bffd1.png)
您最近一年使用:0次
2018-05-04更新
|
718次组卷
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5卷引用:北京五十七中2022届高三10月月考数学试题