名校
解题方法
1 . 已知数列
的前n项和
满足
,
.
(1)求
的通项公式;
(2)若
表示不超过x的最大整数,如
,求
的值;
(3)设
,
,问是否存在正整数m,使得对任意正整数n均有
恒成立?若存在,求出m的最大值;若不存在,请说明理由.
![](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/5211cd2b4ebcdaad8d73cf999b275475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3406792cf683de07aa4371168ad65226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa192e136584c2abab136070a430b9e1.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0ea9bbe51ee5a78c22ad18807ecf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae9df8b3c69acd594e155714263335a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b71732f5f5fb0f70fbccc918948608.png)
您最近一年使用:0次
2 . 设数列
的前
项和为
,且
,数列
满足
,其中
.
(1)证明
为等差数列,求数列
的通项公式;
(2)求数列
的前
项和为
;
(3)求使不等式
,对任意正整数
都成立的最大实数
的值.
![](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/851afb5fa82c3e4448ac7b674d143cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661fb8eb9ebf28433198329f10dbafc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65b4d271ffc3d81da090f03f7d44512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)求使不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47270ec036e4354fd32318aa37e16221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-07-21更新
|
1079次组卷
|
6卷引用:四川省成都市成都市石室中学2021-2022学年高一下学期期末数学试题
名校
解题方法
3 . 已知数列
满足
,
.
(1)证明:数列
为等差数列,并求数列
的通项公式;
(2)若记
为满足不等式
的正整数k的个数,设数列
的前n项和为
,求关于n的不等式
的最大正整数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ad6c0066bd2593d37a0b6b762b7c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b01041691ad489f126f05c18ea8f0fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4680e5e9a6995b82006bde3e8ed402f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45dac5ff2e7b2d374df06d240b5839e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4796ab389935d763a3db9a012d1df3.png)
您最近一年使用:0次
2024-04-22更新
|
600次组卷
|
14卷引用:四川省都江堰中学2019-2020学年高一下学期期中数学试题
四川省都江堰中学2019-2020学年高一下学期期中数学试题(已下线)专题4.6 《数列》单元测试卷(B卷提升篇)-2020-2021学年高二数学选择性必修第二册同步单元AB卷(新教材人教A版,浙江专用)(已下线)江苏省南通市如皋市2022-2023学年高三上学期10月诊断调研测试数学试题(已下线)江苏省南通市如皋市2022-2023学年高三上学期期中模拟数学试题福建省厦门市厦门外国语学校2023届高三上学期期中考试数学试题吉林省长春市长春吉大附中实验学校2022-2023学年高三上学期第四次摸底考试数学试题江苏省镇江市扬中高级中学2022-2023学年高二上学期期末数学试题(已下线)专题1 数列的单调性 微点3 数列单调性的判断方法(三)——倒数比较法(已下线)吉林省长春市长春吉大附中实验学校2023-2024学年高二上学期1月期末数学试题(已下线)期末真题必刷压轴60题(23个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)专题09 数列求和6种常见考法归类(3)山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题(已下线)4.3.2 等比数列的前n项和公式——课后作业(巩固版)(已下线)数列-综合测试卷A卷
名校
解题方法
4 . 高斯是德国著名的数学家,享有“数学王子”的称号,人们把函数
,
称为高斯函数(其中
表示不超过x的最大整数,例如:
,
).已知数列
的首项
,前n项和记为
.若k为函数
,
值域内的任意元素,且当整数
时,都有
成立,则
的通项公式为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e3204e4dc47a448860779349efcedf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ea02e718c638f94174db08de61ea3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1aed47b3da7febc5379a7d46773c9a.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab988b91d5de8edf58c54db012c2e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52eecd38954cd0ca3fb26328a39bb859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf70a562d0cdfa53595c7893d706e46c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
解题方法
5 . 数列
满足
,若
,数列
的前n项和为
,则使不等式
成立的n的最小值为_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5143c81c6b9ebb3c18de8b0e41c1cbe9.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051121063532e79c61b4075ff66a88af.png)
您最近一年使用:0次
6 . 已知数列
满足
,且
,
.
(1)求数列
的通项公式;
(2)若
,求数列
的前
项和
;
(3)设
,记数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633e5b29060ba8615f5f7cb1e207ffff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527bd6adefbb15deb6ad829d7584d072.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df1e8c28789ee186157ec527a7f5199.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)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e6df8a8cd81dffa64bcd405c6d595d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/37c5620fc14efc95fc38c8c3e1792c97.png)
您最近一年使用:0次
2021-08-07更新
|
861次组卷
|
3卷引用:四川省成都市蓉城名校联盟2020-2021学年高一下学期期末联考理科数学试题
四川省成都市蓉城名校联盟2020-2021学年高一下学期期末联考理科数学试题四川省眉山市仁寿第一中学南校区2021-2022学年高二上学期入学考试数学试题(已下线)4.3.3 等比数列的前n项和(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
名校
7 . 若数列
满足“对任意正整数
,
,
,都存在正整数
,使得
”,则称
具有“性质
”.
(1)判断各项均等于
的常数列是否具有“性质
”,并说明理由;
(2)若公比为2的无穷等比数列
具有“性质
”,求首项
的值;
(3)证明首项为2的无穷等差数列
具有“性质
”的充要条件是公差
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4654db8df46552ead8781a1dd2f06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断各项均等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若公比为2的无穷等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)证明首项为2的无穷等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3012337aa392709349731fb1eef5b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1344592c925b273f2cb9b9e47ebbb.png)
您最近一年使用:0次
名校
解题方法
8 . 已知数列
满足
,
,
,
是数列
的前n项和,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25673902449184f5727cbc786aa82a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194463e3b011603ff59c0789bcb65c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1137c7b808293f51f0614ba8de7de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab44ecfed9be29607733d8d0f3431f2f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-09-05更新
|
1320次组卷
|
7卷引用:广东省佛山市南海区2019-2020学年高一下学期期末数学试题
广东省佛山市南海区2019-2020学年高一下学期期末数学试题(已下线)专题7.2 等差数列及其前n项和(精练)-2021年新高考数学一轮复习学与练(已下线)考点42 数列求和-备战2021年新高考数学一轮复习考点逐一攻克江苏省无锡市南菁高级中学2020-2021学年高二上学期(强化班)期中数学试题(已下线)黄金卷19-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)(已下线)第四章 数列-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第二册)第五章 数列(能力提升)-2020-2021学年高二数学单元测试定心卷(人教B版2019选择性必修第三册)
名校
解题方法
9 . 已知
为等差数列
的前
项和,
,
.
(1)求
的通项公式;
(2)求数列
的前
项和
.
![](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/10a051ff41400ce64b47ab5411567ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cb4485663835fc40a9cf82f491d5b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.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
2020-09-01更新
|
1043次组卷
|
8卷引用:四川省绵阳市2019-2020学年高一(下)期末数学试题
10 . 已知数列
满足:
(
)且
,数列
的前n项和
满足:
(
).
(1)证明数列
为等差数列,并求数列
和
的通项公式;
(2)若
,数列
的前n项和为
,对任意的
,
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e63a0b9b65d0819a46d8ec5974cfd94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc93bdea0b85a84179354b598b6f74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1dea28318800c272430a718e28bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e319d8f03ef8178c0823f6cd24038ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
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