1 . 已知数列
的前
项和为
,
.
(1)求
的值;
(2)证明数列
是等比数列,并求出数列
的通项公式;
(3)数列
中是否存在三项,它们可以构成等差数列?(结论不要求证明).
![](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/4eb6457669c73995424232d9ef67983b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e616142cd7122cb7c4e9bc46bb7394.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17d72d1d20d385920c3d9da6bed8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2 .
表示正整数a,b的最大公约数,若
,且
,
,则将k的最大值记为
,例如:
,
.
(1)求
,
,
;
(2)已知
时,
.
(i)求
;
(ii)设
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6294a700967de01e6877d686a0e2e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4160299bf93e7827b97bc5cbb224958e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c95177c5f6454d2de54bb7b0c182ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4b8114fcc770a8512cf03da137ca4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edd29e22f6a7f4d14d9f8d2684d47e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5491950d23d0f3833de05cc3892cacd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a7f848e0002222e3fe290e50301e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ccc57e5668f2a2c1cbc078a767b6855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16edf0bda2c47ed55f471a1838cd03dc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853030075597faf459bec65cd5e0b910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8178596507fe45cea77096a53d6395.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce2bf4a86671ab5cefa4d523d8a0fa2.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beafadba27d9c078bae7761a2b383803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b61920582cc3edd43e273e0cbfa1d4.png)
您最近一年使用:0次
2024-03-26更新
|
1808次组卷
|
8卷引用:广东省佛山市顺德区第一中学西南学校2023-2024学年高二下学期第一次月考数学试卷
广东省佛山市顺德区第一中学西南学校2023-2024学年高二下学期第一次月考数学试卷四川省成都市实验外国语学校2023-2024学年高二下学期第一次阶段考试数学试题辽宁省重点高中沈阳市郊联体2023-2024学年高二下学期4月月考数学试卷(已下线)模块五 专题3 全真能力模拟3(人教B版高二期中研习)(已下线)模块四专题6重组综合练(四川)(8+3+3+5模式)(北师大版高二)福建省泉州市2024届高三质量监测(三)数学试题(已下线)压轴题05数列压轴题15题型汇总-3重庆市第十一中学校2023-2024学年高三第九次质量检测数学试题
名校
解题方法
3 . 去掉正整数中被4整除以及被4除余1的数,剩下的正整数按自小到大的顺序排成数列
,再将数列
中第
项去掉,
中剩余的项按自小到大的顺序排成数列
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3366db77218f27dfa38d90a000d192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8748938373768d7172dc2a8d43ee2d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8139cf70e5af4828821175eb12845a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12b636ded4afe957269d75b6bcfde24.png)
您最近一年使用:0次
2023-02-13更新
|
561次组卷
|
7卷引用:山东省烟台市2022-2023学年高二上学期期末数学试题
名校
解题方法
4 . 对正整数n,函数
是小于或等于n的正整数中与n互质的数的数目.此函数以其首名研究者欧拉命名,故被称为欧拉函数.根据欧拉函数的概念,可得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d605849d6cf6f37b3466ab78ccc95457.png)
______ ,数列
的前n项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc89a53c03cb86fb653bb82128f6cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d605849d6cf6f37b3466ab78ccc95457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9324af97c6bcad0d0954fd7bf9cc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
您最近一年使用:0次
2022-12-14更新
|
454次组卷
|
5卷引用:山西省吕梁市孝义市2022-2023学年高二上学期期末数学试题
山西省吕梁市孝义市2022-2023学年高二上学期期末数学试题河北省定兴中学等校2022-2023学年高二上学期12月联考数学试题辽宁省辽阳市2022-2023学年高三上学期12月月考数学试题(已下线)第六篇 数论 专题2 数论函数 微点2 欧拉函数与Mobius函数山东省德州市2023届高三上学期12月“备考检测”联合调考数学试题
5 . 已知数列
满足
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888bece79cd870b0b067c232c7298c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0b5109a07c54c4562519acefcc309d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb7147e313f9d9f67d19ecb5f499c05.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-11-23更新
|
3523次组卷
|
9卷引用:江苏省扬州中学2022-2023学年高二上学期12月月考数学试题
江苏省扬州中学2022-2023学年高二上学期12月月考数学试题(已下线)求数列的通项公式(已下线)第四章 数列章末重点题型归纳(1)(已下线)专题04 数列(6)河南省豫南九校2022-2023学年高三上学期第一次联考数学(文)试题(已下线)专题5 数列 第2讲 数列通项与求和(已下线)模块三 大招3 分式结构递推高三文数试题-河南省豫南六校2022-2023学年高三上学期第一次联考试题河南省许昌市禹州市高级中学2024届高三上学期第四次阶段性考试(期末)数学试卷
名校
解题方法
6 . 已知数列
的前
项和为
,且满足
,当
时,
.
(1)计算:
,
;
(2)证明
为等差数列,并求数列
的通项公式;
(3)设
,求数列
的前
项和
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317e67653c0733cd4e7b7dd6cec3b8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7ae2cdce39d8ecb11fda2306edf688.png)
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2617bb1f8a9a091ce2c35872295e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70450eccc9c798f35682ec650450fc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ac0dc2cf85bd5a6e6061e17ec8c7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-08-14更新
|
1572次组卷
|
7卷引用:四川省广安市武胜烈面中学校2021-2022学年高二上学期数学(理)入学考试试题
四川省广安市武胜烈面中学校2021-2022学年高二上学期数学(理)入学考试试题湖北省武汉市江岸区2022-2023学年高二上学期期末数学试题湖北省武汉市华中科技大学附属中学2022-2023学年高二下学期2月月考数学试题(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)第04讲 数列求和(练)
解题方法
7 . 已知集合
,
.
中的所有元素按从小到大的顺序排列构成数列
,
为数列
的前
项的和.
(1)求
;
(2)如果
,
,求
和
的值;
(3)如果
,求
(用
来表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20f018e0d510b8446509a912f8db0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb09edea21e214eb96a7b121855c8cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3cf6f2bbe20a404fea41a4d2b1c4c7.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30909f32d34cac6422481a60917475c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d65f106479ae794e4fd54f6797424f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e9007ddcca8c1eac1924d2db796e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcab407cb46d9a721098b04f085a248f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
8 . 已知数列
中的相邻两项
,
是关于
的方程
的两个根,且
.
(1)求
,
,
,
;
(2)求数列
的前
项和
;
(3)记
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7b6ecfdff9d2b29ef64d2a6f3343f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e17c3925955291056e16a4e075b3a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23195d199724aea88a760a0ae35ff9b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd71bc7e6668f90f259ad0b06dd60c2.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a742c7b44a3b6ebbbe78d5e0ad04bca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e01c1fac9f9ed8d588d4e85c0db8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3e29cafd6334eca70149f61f34ca7c.png)
您最近一年使用:0次
2021-10-21更新
|
724次组卷
|
2卷引用:上海市复兴高级中学2021-2022学年高二上学期10月质量检测数学试题
名校
解题方法
9 . 数列
是公差为
的等差数列,数列
是公比为
的等比数列,记数列
的前
项和为
.已知
.
(1)若
(
是大于2的正整数)求证:
;
(2)若
(
是某个确定的正整数),求证:数列
中每个项都是数列
的项.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/b4fdab09813d10249e0f169a8abbc051.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fa1d84e33943f4947d4dec19f80f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee956329e95a172d86c86b2f6af7aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce13be3cf67126a906396ba8ca32721.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3d147fce4a375081f49692790b81bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2020-11-15更新
|
309次组卷
|
4卷引用:江苏省苏州市昆山市2020-2021学年高二上学期期中教学质量调研测试数学试题
名校
10 . 意大利著名数学家斐波那契在研究兔子繁殖问题时,发现有这样一列数:1,1,2,3,5,….,其中从第三项起,每个数等于它前面两个数的和,后来人们把这样的一列数组成的数列
称为“斐波那契数列”,记
为数列
的前n项和,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-02-01更新
|
1340次组卷
|
6卷引用:山东省菏泽市2019-2020学年高二上学期期末数学试题
山东省菏泽市2019-2020学年高二上学期期末数学试题江苏省苏州市第一中学2020-2021学年高二上学期期初数学试题(已下线)专题07 数列-备战2020年新高考数学新题型之【多选题】-《2020年新高考政策解读与配套资源》(已下线)专题07 数列(1)-2020年新高考新题型多项选择题专项训练(已下线)专题7.1 数列的概念与简单表示(精练)-2021年新高考数学一轮复习学与练江苏省南京市金陵中学2020-2021学年高三上学期8月学情调研测试数学试题