名校
解题方法
1 . 在1,3中间插入二者的乘积,得到1,3,3,称数列1,3,3为数列1,3的第一次扩展数列,数列1,3,3,9,3为数列1,3的第二次扩展数列,重复上述规则,可得1,
,
,…,
,3为数列1,3的第n次扩展数列,令
,则数列
的通项公式为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ca222d3f8f34fb6b4b385f7f5c699f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13a9ce5fc6e3fdc06fce427f6e0571e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
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|
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|
6卷引用:新题型01 新高考新结构二十一大考点汇总-1
(已下线)新题型01 新高考新结构二十一大考点汇总-1(已下线)压轴题数列新定义题(九省联考第19题模式)练江西省九师联盟2024届高三上学期1月质量检测试数学试题江西省宜春市上高二中2024届高三上学期期末数学试题黑龙江省大庆市大庆中学2024届高三下学期开学考试数学试题广东省广州市执信中学2023-2024学年高二下学期3月月考数学试题
解题方法
2 . 数列
定义如下:
,
,若对于任意
,数列的前
项已定义,则对于
,定义
,
为其前n项和,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e5160ff110a19878e4fae639319e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4777ee11e9f2737b4bc188d779fe54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b4a942504cad77a24459b6c6b0bbfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.数列![]() ![]() ![]() | B.数列![]() ![]() |
C.数列![]() ![]() ![]() | D.![]() |
您最近一年使用:0次
3 . 若存在常数
,使得数列
满足
(
,
),则称数列
为“
数列”.
(1)判断数列:1,2,3,8,49是否为“
数列”,并说明理由;
(2)若数列
是首项为
的“
数列”,数列
是等比数列,且
与
满足
,求
的值和数列
的通项公式;
(3)若数列
是“
数列”,
为数列
的前
项和,
,
,试比较
与
的大小,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2108ef893c3ef1f8599a4b8ba7083e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e91406484c332ac8fc96a54c7e187b.png)
(1)判断数列:1,2,3,8,49是否为“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3331574262d23e775c78e1806dd38a.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e91406484c332ac8fc96a54c7e187b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e909fec4d31cce0e352edd6186d7c235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e91406484c332ac8fc96a54c7e187b.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4a42272d8dfd41ed6f6594f8c82c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07812c89c11b5cb96c2eb573e681cbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1f6e5fb3d02ed5fe61763857e80c43.png)
您最近一年使用:0次
2023-12-14更新
|
1324次组卷
|
10卷引用:2024年高考数学全真模拟卷05(新题型地区专用)
(已下线)2024年高考数学全真模拟卷05(新题型地区专用)(已下线)黄金卷05(已下线)新高考预测卷(2024新试卷结构)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编(已下线)专题05 数列(四大类型题)15区新题速递(已下线)专题09 导数(三大类型题)15区新题速递(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题16-19上海市普陀区2024届高考一模数学试题2024届高三新改革数学模拟预测训练二(九省联考题型)湖南省长沙市四县区2024届高三下学期3月调研考试数学试卷
4 . 帕多瓦数列是与斐波那契数列相似的又一著名数列.在数学上,帕多瓦数列被以下递推的方法定义:数列
的前
项和为
,且满足:
.则下列结论正确的是( )
![](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/7e5c3c72c9b357d00671073d8befacea.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-01-15更新
|
1349次组卷
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7卷引用:专题9 周期数列 微点2 周期数列的“脸谱”识别
(已下线)专题9 周期数列 微点2 周期数列的“脸谱”识别(已下线)专题11 数列前n项和的求法 微点10 数列前n项和的求法综合训练(已下线)数列新定义专题01数列的概念山东省济宁市2022-2023学年高三上学期期末数学试题广东省普宁市华美实验学校2022-2023学年高二下学期第一次月考数学试题(已下线)模块三 专题3 题型突破篇 小题满分挑战练(1)
名校
解题方法
5 . 若一个数列的奇数项为公差为正的等差数列,偶数项为公比为正的等比数列,且公差公比相同,则称数列为“摇摆数列”,其表示为
,
,
,若数列
为“摇摆数列”且
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cb519a2ad653cbd8e565687a7c0a86.png)
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.(注:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a43121706692bcbc51e3d2a177b5839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d0919893474b813ff79a073cd69cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b17db8c17aecaa3991045048a758513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b037d2c4d975cb847c72b83e717860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd2edf101d891d5471a0848ebbcf65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cb519a2ad653cbd8e565687a7c0a86.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63ce2096afea66022f5ff11bc763a8e.png)
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|
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|
3卷引用:重难点10 数列的通项、求和及综合应用【九大题型】
名校
6 . 已知:
为有穷正整数数列,其最大项的值为
,且当
时,均有
.设
,对于
,定义
,其中,
表示数集M中最小的数.
(1)若
,写出
的值;
(2)若存在
满足:
,求
的最小值;
(3)当
时,证明:对所有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3665eb490a4be3b7b1a98238753899ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f927412b623486cde0d3f7d8aa8f264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6026d3efaa278220e3553d9802402bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2555a7889a95a7c4f8817340843c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb413e11e509aa1118694ad662785ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e934982c8340194b4396399b7f4b24bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d51777d3fca1ee8f588a6c39190dae.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1ae4b6456261b2948255780c39de17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c65edaa726a93d0600b7bb0a9bcc2ad.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb995c875a663dc8e907ba2d22ff7af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624bef0b515a06caf80cd3b7a3161aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb8b473e53c4f073f717eabe1d33f4.png)
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2024-04-09更新
|
1131次组卷
|
4卷引用:2024年北京高考数学真题平行卷(提升)
(已下线)2024年北京高考数学真题平行卷(提升)北京市海淀区2024届高三下学期期中练习(一模)数学试题2024届河北省雄安新区部分高中高考三模数学试题甘肃省白银市靖远县第一中学2024届高三下学期模拟预测数学试题
7 . 设整数
满足
,集合
.从
中选取
个不同的元素并取它们的乘积,这样的乘积有
个,设它们的和为
.例如
.
(1)若
,求
;
(2)记
.求
和
的整式表达式;
(3)用含
,
的式子来表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c4b8f96da2495ecc059119eb01e0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7601dbefa6836756e3d2731b79af0126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8086c293be0cdc3a19d585bbe148da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdea830c734212c9831f428918636e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfd4e75e49d369dcc3e961c6b58eafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34dac6973b2d824ea18182ebaac82284.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d7245bd8cc47b87eeb270d4f39ee4b.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55746d3923c7cf11339076311286165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f5dcdd63776d5b10d1e5612abdaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065724f62f61254af999bb5a7c9beb95.png)
(3)用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86582734340e1b08498b0645d85a55b.png)
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2024-02-27更新
|
1264次组卷
|
3卷引用:压轴题05数列压轴题15题型汇总-2
8 . 对于数列
,由
作通项得到的数列
,称
为数列
的差分数列,已知数列
为数列
的差分数列,且
是以1为首项以2为公差的等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0d1acb1b90f596ce30595b9ee06b25.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0d1acb1b90f596ce30595b9ee06b25.png)
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2023-11-03更新
|
1185次组卷
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7卷引用:专题09 数列的通项公式、数列求和及综合应用(练习)-2
(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-2山东省德州市2024届高三上学期适应性联考(一)数学试题(已下线)模块一 专题5《等差数列与等比数列》单元检测篇 B提升卷 期末终极研习室(高二人教A版)广东省广州市广东实验中学2024届高三上学期第一次调研数学试卷江苏省镇江市丹阳高级中学2024届高三下学期2月阶段检测数学试题(已下线)模块一专题1《数列基础、等差数列和等比数列》单元检测篇B提升卷(高二下人教B版)(已下线)模块一 专题2《数列基础、等差数列和等比数列》单元检测篇B提升卷(高二北师大版)
名校
9 . 设
为给定的正奇数,定义无穷数列
:
若
是数列
中的项,则记作
.
(1)若数列
的前6项各不相同,写出
的最小值及此时数列的前6项;
(2)求证:集合
是空集;
(3)记集合
正奇数
,求集合
.(若
为任意的正奇数,求所有数列
的相同元素构成的集合
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77576292d833c93bdcf4da9787ee0db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003dd0feaa12a01db4c777784889c374.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3884cadaff5a78756698d57c41f305d.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611448a63d973f73f8c0026dd38ac932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7dbf7c1220f9db7d313570143f4a709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2023-12-21更新
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5卷引用:专题1 集合新定义题(九省联考第19题模式)练
(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)4.3 数列-求数列通项的八种方法(八大题型)(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)拔高点突破01 集合背景下的新定义压轴解答题(四大题型)北京市西城区北师大附属实验中学2024届高三上学期12月月考数学试题湖南省2024届高三数学新改革提高训练二(九省联考题型)
10 . 对正整数
,设数列
.
是
行
列的数阵,
表示
中第
行第
列的数,
,且
同时满足下列三个条件:①每行恰有三个1;②每列至少有一个1;③任意两行不相同.记集合
或
中元素的个数为
.
(1)若
,求
的值;
(2)若对任意
中都恰有
行满足第
列和第
列的数均为1.
①
能否满足
?说明理由;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3900a6f09149151f7d8479912e1a48e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1430ce165611dfc92e924a1cdc6c8220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223f93ed43c7772a367043ae224b75da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c734e1b65651e598e1a907a041664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51c223d60883c551607e8b6e8d7fd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2dce4d63752586495edc8d58dfc45bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cde6077954017c6ac884c0e76662c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224dcfa6dae1dc0511ad72da8617283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2c5e187752ef828b307951da554bb.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32708eeade6cbb36e1dfda113eececd0.png)
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