解题方法
1 . 数列
满足
且
,
,
,
构成等差数列.
(1)试求出所有三元实数组(α,β,γ),使得
为等比数列.
(2)若
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f390f47fa5678c9a165c50fb9dec58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be536a2097ded867adac5edebb79906b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e6820c50fa2aa589de5331d7d5f950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13739ca823d61005798cc3298400c6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad28237c0f9ca65341101d9d7e73e73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
(1)试求出所有三元实数组(α,β,γ),使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4623bc660145c6ff98af7b1753d5357a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
您最近一年使用:0次
23-24高三上·广东深圳·阶段练习
名校
解题方法
2 . 已知数列
的首项不为0,前
项的和为
,满足
.
(1)证明:
;
(2)若
,证明:
;
(3)是否存在常数
,使得
为等比数列?若存在,求出
的所有可能值;若不存在,说明理由.
![](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/9397a90e4ea953c72b03e20133870979.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4176db941f1af7fcda4ee86c03427f63.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbaa33825e93751c26b463890ac672a.png)
(3)是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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3 . 高斯是德国著名数学家,近代数学的奠基者之一,享有“数学王子”的称号,用他名字定义的函数
称为高斯函数,其中
表示不超过x的最大整数,如
,
,已知数列
满足
,
,
,若
,
为数列
的前n项和,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1550a97c21c1d71c9e95dde569668be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54a0e82778f606d95a486835ac9f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f2323cbdf0b1b71092c962ae705102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d845281cd834068104af1b1aa6027c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7231e303ae39572f6c359c5e83822075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5735a391a46cfdbd63e171769f8abb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c3ac959bdf1b78cb98d92b87c91c46.png)
A.2026 | B.2025 | C.2024 | D.2023 |
您最近一年使用:0次
2023-11-25更新
|
921次组卷
|
7卷引用:4.3.2 等比数列的前n项和公式——课后作业(巩固版)
(已下线)4.3.2 等比数列的前n项和公式——课后作业(巩固版)云南省曲靖市第一中学2022-2023学年高一下学期7月期末考试数学试题江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题内蒙古赤峰市赤峰二中2024届高三上学期第三次月考数学(理)试题(已下线)第五章 数列 专题8 数列中的递推(已下线)第五章 数列 专题7 有关数列求通项、周期性求和的问题陕西省西安市西安中学2024届高三上学期期末数学(理)试题
名校
4 . 已知
是无穷数列,
,
,且对于
中任意两项
,
,在
中都存在一项
,使得
.
(1)若
,
,求
;
(2)若
,求证:数列
中有无穷多项为0;
(3)若
,求数列
的通项公式.
![](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/a55ef34345210312db273ab4981c40f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0616dca5cf0229b9f801365cc2bcfff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba50a82a53f0e597c096ccf5746f1b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53abaaac2e62f510d996e6db22aefe7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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5 . 设数列
,即当
时,
.记
.
(1)写出
,
,
,
;
(2)令
,求数列
的通项公式;
(3)对于
,定义集合
,求集合
中元素的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa7b3c190459af645f8bfb2d287fcde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808d924a0869b4fd83c2af3a9c08c755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21d7086ab24e85a3a109596d2112065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48990b6e63ba2d3697523faab15d4846.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2714e51cd5b5f0529bcad6499c1b9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
(3)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b04dd5926d27d2fe7c375030018df26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0720f874c2f8b28c8c289dddb362f336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d88909e5fcc68bc96d756f2d65060c.png)
您最近一年使用:0次
解题方法
6 . 已知
是数列
的前
项和,
,则( )
![](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/b5d111e1236fa8bd7916f7b1f2fe2afe.png)
A. ![]() |
B. ![]() |
C. 当![]() ![]() |
D. 当数列![]() ![]() ![]() |
您最近一年使用:0次
2022-09-03更新
|
1600次组卷
|
5卷引用:4.2.2 等差数列的前n项和公式(同步练习)-【一堂好课】2022-2023学年高二数学同步名师重点课堂(人教A版2019选择性必修第二册)
(已下线)4.2.2 等差数列的前n项和公式(同步练习)-【一堂好课】2022-2023学年高二数学同步名师重点课堂(人教A版2019选择性必修第二册)江苏省百校联考2022-2023学年高三上学期第一次考试数学试题湖北省武汉市第十九中学2023届高三上学期11月线上月考数学试题第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)专题10 数列通项公式的求法 微点1 观察法(不完全归纳法)、公式法
名校
解题方法
7 . 对于有限数列
,
,
,
,定义:对于任意的
,
,有:
(i )
;
(ii )对于
,记
.对于
,若存在非零常数
,使得
,则称常数
为数列
的
阶
系数.
(1)设数列
的通项公式为
,计算
,并判断2是否为数列的4阶
系数;
(2)设数列
的通项公式为
,且数列
的
阶
系数为3,求
的值;
(3)设数列
为等差数列,满足-1,2均为数列
的
阶
系数,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddcdb2da504ba468d10e26134b46327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d7da87286b3dd83f0e7d4e5b496eac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c70fdfa2d88876d54feb6d890204e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5d5bdce735c2dbe4bc07727c119459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
(i )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8329865917b8a177cafbba3c80ee1563.png)
(ii )对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686b332872c51b433befe65fbe773380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4632dd98afcce0d49f5f4b438dab024d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da493db80b421a09904f1aea6a8576a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a89d99d11a58a2e6ac83d0d6d2a5119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18841a2d420196560e6d4df505cc4063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb42a8b2956bcbdc702f2675862405b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设数列
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8040c494c55340314d0681aaa5a0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2022-03-11更新
|
1154次组卷
|
14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)北京市昌平区2021届高三二模数学试题北京市顺义区第一中学2022届高三10月月考数学试题上海市实验学校2022届高三下学期开学考试数学试题北京市一六一中学2022届高三2月自主测试数学试题北京市2022届高三普通高等学校招生全国统一考试数学模拟试题北京市西城区第一六一中2021-2022学年高三下学期开学数学试题北京市海淀区首都师范大学附属中学2023届高三下学期2月阶段性质量检测数学试题(已下线)4.3.2.2 等比数列的前n项和的性质及应用(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)北京卷专题18数列(解答题)北京市一六一中学2022届高三下学期开学考数学试题北京市第五十五中学2023-2024学年高二上学期期中调研数学试题(已下线)专题03 条件存在型【讲】【北京版】2北京理工大学附属中学2023-2024学年高二下学期期中考试数学试卷
名校
8 . 设整数数列
,
,…,
满足
,
,且
,
,则这样的数列的个数为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91870d50905112295ccb9287ebb8f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7595888a4f3632ac396247d7012dd998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71481243c145e96b64017f86b74143ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff3f51902e1270db756839c94ce7ec5.png)
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2021-10-14更新
|
1294次组卷
|
5卷引用:6.2.3组合-6.2.4组合数——课时作业(提升版)
(已下线)6.2.3组合-6.2.4组合数——课时作业(提升版)上海市2022届高三上学期一模暨春考模拟卷(三)数学试题(已下线)专题12 计数原理(理)上海市格致中学2023届高三上学期12月月考数学试题(已下线)专题9-3 排列组合19种归类(理)(讲+练)-4
名校
9 . 已知数列
满足
,
,若
为周期数列,则
的可能取到的数值有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5319ade23e57d6513f39194f9372e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fa86a6fe03bc72813bb18cc5cb7172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
A.![]() | B.![]() | C.![]() | D.无数个 |
您最近一年使用:0次
2020-11-15更新
|
1466次组卷
|
4卷引用:苏教版(2019) 选修第一册 一蹴而就 第4章 单元整合
苏教版(2019) 选修第一册 一蹴而就 第4章 单元整合上海市奉贤区曙光中学2021届高三上学期期中数学试题上海市曹杨第二中学2020-2021学年高二上学期期末数学试题(已下线)课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)
10 . 已知n∈N*,数列{an}的前n项和为Sn,且Sn=an+1﹣a1;数列{bn}的前n项和为Tn,且满足Tn+bn=n+
,且a1=b2.
(1)求数列{an}的通项公式;
(2)求数列{bn}的通项公式;
(3)设cn=
,问:数列{cn}中是否存在不同两项ci,cj(1≤i<j,i,j∈N*),使ci+cj仍是数列{cn}中的项?若存在,请求出i,j;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492ec5a0383c89c901f3ea4c5c6890e0.png)
(1)求数列{an}的通项公式;
(2)求数列{bn}的通项公式;
(3)设cn=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462f644c4a74b81d24687e3fc613ec54.png)
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