名校
解题方法
1 . 约数,又称因数.它的定义如下:若整数
除以整数
得到的商正好是整数而没有余数,我们就称
为
的倍数,称
为
的约数.设正整数
共有
个正约数,即为
,
,
,
,
.
(1)当
时,若正整数
的
个正约数构成等比数列,请写出一个
的值;
(2)当
时,若
,
,
,
构成等比数列,求正整数
的所有可能值;
(3)记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87484a879f450ab097f720fb2a0f4a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c0cd13ec90e5697013e59d73d3e82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afeed05dbd9752dd537a06bbcbc867cf.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeaed9ec21e090defafcfeefe0059c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe164d8a8a4049e01565b576007651de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01416ee1d48b17f889e444b7eda99740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a49832d7c33597639bea9eace7989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57e391b1d575796894fea80cce6329b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04bc6dcaef3c78886e21f1c41e7f2cd6.png)
您最近一年使用:0次
2024-05-04更新
|
164次组卷
|
12卷引用:北京市通州区2023届高三上学期期末数学试题
北京市通州区2023届高三上学期期末数学试题北京市第五十五中学2024届高三上学期10月月考数学试题北京市东城区第六十五中学2024届高三上学期12月月考数学试题广东省广州市广东实验中学2023-2024学年高三下学期教学情况测试(二)数学试卷A湖南省长沙市雅礼中学2024届高三一模数学试卷(已下线)高考数学冲刺押题卷02(2024新题型)(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06 数列(已下线)第四套 艺体生新高考全真模拟 (一模重组卷)湖南省常德市第一中学2023-2024学年高二下学期第一次月考数学试题北京市西城区北京师范大学第二附属中学2023-2024学年高二下学期期中考试数学试题(已下线)高二下学期第三次月考模拟卷(新题型)(范围:导数+选择性必修第三册)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第三册)
2 . 已知数列
满足:
;
;
,
,其中
,
.数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
____________ ,令
,则数列
的前n项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2669d696ea9194aa530835db09909c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d046ec9d9aaac508a16462f2980ca18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c68b253787b7980d259a243ee42ecfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917482bcd9948fdd030dd86b51f585c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ced55125101a813dd26072af98b97f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd9e2298ae0163ba37bd06e716210c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
的通项公式为
,若对任意
,不等式
恒成立,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed05011f108dad0b561425463d5aae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5596a2e2c7d1cc91c37d397939027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-02-14更新
|
466次组卷
|
4卷引用:安徽省部分学校2024届高三上学期期末质量检测数学试题
4 . 已知数列
满足
,且对任意正整数m,n都有
.
(1)求数列
的通项公式;
(2)求数列
的前n项和
,若存在正整数k,使得
,求k的值;
(3)设
,
是数列
的前n项和,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598e934b63b96d7fddb52d21d3682870.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3149c2c5402c5a686047b798a20a3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab5a616a68a635ae7499b5608870bfd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472280dfeec0c5087942f47ceb5ead63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f43bb7c0b9b431c30823978bff49c9.png)
您最近一年使用:0次
名校
解题方法
5 . 已知为数列
的前
项和,且
,若
,
,
是
的前
项和,求
.
您最近一年使用:0次
2024-01-12更新
|
865次组卷
|
2卷引用:黑龙江省海林市朝鲜族中学2023-2024学年高二上学期第三次考试(期末)数学试卷
6 . 已知数列满足
为数列
的前
项和,则下列说法正确的有( )
A.当![]() ![]() |
B.设![]() ![]() ![]() ![]() ![]() |
C.设![]() ![]() ![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
7 . 已知
是等差数列
的前
项和,满足
,设
,数列
的前
项和为
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e51bd048ce07c3d52e414ba46be23a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230ae9538a1b0ec62c3491cbce25df8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af0d8d4f6e5b80bcb510173c5802358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.![]() | B.使得![]() ![]() |
C.![]() | D.当![]() ![]() |
您最近一年使用:0次
2023-11-29更新
|
994次组卷
|
4卷引用:模块三 专题3 小题满分挑战练(2) 期末终极研习室(高二人教A版)
(已下线)模块三 专题3 小题满分挑战练(2) 期末终极研习室(高二人教A版)(已下线)第06讲:数列求和 (必刷5大考题+5大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)中学生标准学术能力诊断性测试(THUSSAT)2023-2024学年高三上学期11月测试数学试卷山西省朔州市怀仁市2023-2024学年高二上学期第二次教学质量调研数学试题
2023·全国·模拟预测
名校
解题方法
8 . 已知数列
满足
,
且
,若
,数列
的前
项和为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf093e5d54c8725f0377fcdf153a0bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dedcd0d35f3708402c208a01935b8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4cecbdebeb5d12fbe1d54b81cc05a8.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3200f3cc24af2c9663b5c0de282810.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-20更新
|
1163次组卷
|
7卷引用:模块六 全真模拟篇 能力2 期末终极研习室(2023-2024学年第一学期)高三
(已下线)模块六 全真模拟篇 能力2 期末终极研习室(2023-2024学年第一学期)高三(已下线)2024年普通高等学校招生全国统一考试文科数学领航卷(五)江苏省苏州市西交苏州附中(纳米班)2023-2024学年高二上学期12月月考数学试题黑龙江省哈尔滨师范大学附属中学2023-2024学年高二上学期期末考试数学试题江苏省盐城市五校联盟2023-2024学年高二上学期1月期末考试数学试题广东省汕头市金山中学2023-2024学年高二上学期期末考试数学试题湖南省永州市第一中学2023-2024学年高二下学期开学检测数学试题
解题方法
9 . 已知数列
的通项公式为
,数列
满足
.
(1)求
的通项公式;
(2)设
,记数列
.的前
项和为
,从下面两个条件中选一个,判断是否存在符合条件的正整数
,
,
,若存在,求出
,
,
的一组值;若不存在,请说明理由.
①
,
,
成等比数列且
,
,
成等比数列;
②
,
成等差数列且
,
,
成等差数列.
注:如选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e029720d8eafb27636ccf2e2fbbb36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/537f6573f8f0f7ce9ce8a573764b3d67.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73dce2c1f85be0668fbf9051fe6bebca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42ba3c69c215c8f25c820c6c8f44e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/1254067b56565394384de5be7b8f3ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ffd3e122e6c12db948aeedaea20fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ea6b40e950f60a41b5810445cdb83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31ec8dee46f3affe69cbdb2abbe8feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b096e3e4bb5950794a74ec46a53151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71cdb539824e764a9d71d28e3181f42.png)
注:如选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2023-11-15更新
|
744次组卷
|
5卷引用:模块三 专题8 大题分类练 劣构题专练 拔高 期末终极研习室高二人教A版
(已下线)模块三 专题8 大题分类练 劣构题专练 拔高 期末终极研习室高二人教A版江西省2024届高三上学期11月一轮总复习调研测试数学试题(已下线)专题01 条件开放型【练】【通用版】2024届河南省名校学术联盟高考模拟信息卷&押题卷数学(三)(已下线)专题6.2 等比数列及其前n项和【十大题型】
10 . 已知数列
的前n项和为
,
,且
.
(1)证明:数列
为等比数列,并求其通项公式;
(2)若______,求数列
的前n项和
.
从①
;②
;③
,这三个条件中任选一个补充在上面的横线上并解答问题.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4424ac7dd09b764226ab6ff9e36564.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若______,求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5b5451f8f8bd987d61b67cb29ef676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dece09ce17894e8c4c1b2fa03ba26496.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次