1 . 已知数列
满足
,
,令
,设数列
前n项和为
.
(1)求证:数列
为等差数列;
(2)若存在
,使不等式
成立,求实数
的取值范围;
(3)设正项数列
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8363902560fce392e05042b7287929a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacbbf38ec1b411cfd9693874bebd4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb3185977be193745f403547d1e9800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8261beeefacd521644faf4658227a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)设正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d1dbbe083e1e1672b2439ea746d976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf47abf4f5649d379a8a69983a3fc56.png)
您最近一年使用:0次
2022-07-21更新
|
1594次组卷
|
7卷引用:四川省眉山市2021-2022学年高一下学期期末数学(理)试题
四川省眉山市2021-2022学年高一下学期期末数学(理)试题广东省广东实验中学2023届高三上学期第一次段考数学试题(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)4.2.2.2 等差数列的前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)(已下线)专题15 数列不等式的证明 微点6 数列不等式的证明综合训练(已下线)数列与不等式(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)
2 . 正项数列
的前n项和为
,
,则
( )其中
表示不超过x的最大整数.
![](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/900f88d57c8799d3694a7ce6c1ccfcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65da53813e3fa71bac506068882813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fab6009ffb15a88bd843a1c2b8d7770.png)
A.18 | B.17 | C.19 | D.20 |
您最近一年使用:0次
2022-04-08更新
|
998次组卷
|
5卷引用:四川省宜宾市第四中学校2023-2024学年高二上学期期末数学试题
四川省宜宾市第四中学校2023-2024学年高二上学期期末数学试题新疆石河子市第一中学2022届高三3月第一周模拟数学(理)试题(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)(已下线)4.1 等差数列(第1课时)(十大题型)(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)【讲】专题2 构造数列问题
名校
解题方法
3 . 已知函数
,满足:①对任意
,都有
;
②对任意
都有
.
(1)试证明:
为
上的单调增函数;
(2)求
;
(3)令
,试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604c3ed013411e9434f9b09044231465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2c2b34f9a5a85e9e2d4057b3c10130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf6a72e9fa5c736a96163d1628cebb6.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407169706c508bfae5d039639b49477d.png)
(1)试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd62e0e1189886f90e0c5bc126f64a4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cf16d7b4f5f2f8d6a1fe2d8a59538b.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2f851b643e3a77682f0196dcf3e797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fe881244327001ef94b611e6b159db.png)
您最近一年使用:0次
解题方法
4 . 已知数列
满足
.
(1)求数列
的通项;
(2)设
,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c811b8b0124c799580b5fa9cae3929.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980d51ba3340a31964fbec9e6f243ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcbc64b0f3d08d5285ee32e5ca13d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6afc5de00034c4b65e5c2841c1e299.png)
您最近一年使用:0次
名校
5 . 已知函数
.
(1)求证:
有且仅有2个零点;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6455627b11abd2e73577e254cd383e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cb44fbeaa02d6063a725af4b76b6a3f.png)
您最近一年使用:0次
2020-07-23更新
|
605次组卷
|
2卷引用:四川省射洪中学校2023届高三下学期第一次月考理科数学试题
名校
解题方法
6 . 已知数列
和
满足
,且对任意的
,
,
.
(1)求
,
及数列
的通项公式;
(2)记
,
, 求证:
,
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa4921de71ae60a9ba615904a419136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86299c91ec5ecbd34533dd1efaac5b3c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1c5b2b3f32f3f95b1dddd62686d89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94b99c2327b08f8b343e079282d7d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
您最近一年使用:0次
2020-07-22更新
|
392次组卷
|
2卷引用:四川省资中县第二中学2022-2023学年高二上学期开学考试理科数学试题
名校
7 . 已知数列
满足:
,
,
前
项和为
的数列
满足:
,
,又
.
(1)求数列
的通项公式;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9042ea58c80eab852af7fe72980d4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ba2efb4674cbc52ce744836fb0e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86795d9c9488ebced9be6a899a55dd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab548a0fd7eb2c1949ad3d797480f9c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b13a36fc42d03746ea33dbd64d3cc54.png)
您最近一年使用:0次
2020-05-15更新
|
526次组卷
|
3卷引用:四川省乐山第一中学校2019-2020学年高一下学期期中数学试题
解题方法
8 . 设
,
,
,
.
(1)若
的最小值为4,求
的值;
(2)若
,证明:
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70cecfc37310dd869b0d51ff44d64e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c88f4308b66716ffe5df610b5dfb7d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93718bc80266ccc70bbdacdcad2e738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1530d6081c3fa517f04a73079ec2a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e921e4e730669eeca4baafc3b57d7a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
您最近一年使用:0次
2020-04-21更新
|
583次组卷
|
3卷引用:2020届四川省高三大数据精准教学第一次统一监测文科数学试题
名校
解题方法
9 . 已知函数
.
(1)求不等式
的解集;
(2)设函数
的最小值为m,当a,b,
,且
时,求
的最大值.
![](https://img.xkw.com/dksih/QBM/2020/3/9/2415737295060992/2416062545199104/STEM/34c49c58bd714133920bb56a98d7f14a.png?resizew=177)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4509817be39bef4bcde115996ee39e8.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac49619543ace1f24754240fcf6cb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86be2de99fbf7f99cd54ab399146b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e644e75022aa5372e81410c95f393b10.png)
您最近一年使用:0次
2020-03-09更新
|
991次组卷
|
15卷引用:2020届四川省泸县第一中学高三下学期第一次在线月考数学(理)试题
2020届四川省泸县第一中学高三下学期第一次在线月考数学(理)试题2020届四川省泸县第一中学高三下学期第一次在线月考数学(文)试题【省级联考】东北三省四市2019届高三第一次模拟数学(文)试题【市级联考】东北三省四市2019届高三第一次模拟数学(理)试题1【市级联考】辽宁省大连市2019届高三第一次模拟考试数学(理)试题【市级联考】东北三省四市2019届高三第一次模拟数学(理)试题2【市级联考】东北三省四市2019届高三第一次模拟数学(文)试题【市级联考】吉林省长春市普通高中2019届高三质量检测(三)数学(理)试题【市级联考】吉林省长春市普通高中2019届高三质量检测(三)数学(文科)试题江西省南昌市第二中学2019-2020学年高三第四次月考数学(文)试题河北省石家庄市第二中学(南校区)2019-2020学年高三下学期教学质量检测模拟数学(理)试题2020届湖南省长沙市长郡中学高三下学期4月第三次适应性考试数学(文)试题(已下线)理科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)文科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)专题23 不等式选讲-2020年高考数学(文)母题题源解密(全国Ⅲ专版)
名校
10 . 设数列
的前n项和为
.满足
,且
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3219353c9f4d45d0a1562102a4eb9fb8.png)
(1)求数列
的通项公式;
(2)证明:对一切正整数n,有
.
![](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/c8a4e5523dffbdc4f0fa2213f89ce771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3219353c9f4d45d0a1562102a4eb9fb8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:对一切正整数n,有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab5128a0393c0a1dce8af96f24de54f.png)
您最近一年使用:0次
2019-05-20更新
|
634次组卷
|
4卷引用:四川省绵阳中学2022-2023学年高三上学期期末模拟检测试题