名校
解题方法
1 . 若数列
满足“对任意的正整数i,j,
,都存在正整数k,使得
”,则称数列
具有“性质P”.
(1)判断数列
和
是否具有“性质P”,并说明理由;
(2)若公比为
的无穷等比数列
具有“性质P”,求首项
的取值集合;
(3)若首项
的无穷等差数列
具有“性质P”,求公差d的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4654db8df46552ead8781a1dd2f06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15ffa7fecea3704dc892ea8cd513c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd08688cf3fe3b888ece29a6b22152b2.png)
(2)若公比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)若首项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
2 . 集合
,集合
,若集合
中元素个数为
,且所有元素从小到大排列后是等差数列,则称集合
为“好集合”.
(1)判断集合
、
是否为“好集合”;
(2)若集合
是“好集合”,求
的值;
(3)“好集合”
的元素个数是否存在最大值?若存在,求出最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be119f90345add00cd53fa449fe6f04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0672043affad9fdac675ce9dd823228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09b60535bb9fec40ebca4fb3f53adb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cc522867a8598c9a014c9eb33864e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4372e587e4438cd61dc2a564b68d01e.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab0d982114b3cfb6e4316ae3b1c7c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)“好集合”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2021-05-26更新
|
1041次组卷
|
5卷引用:第一章 集合(选拔卷)-【单元测试】2021-2022学年高一数学尖子生选拔卷(苏教版2019必修第一册)
(已下线)第一章 集合(选拔卷)-【单元测试】2021-2022学年高一数学尖子生选拔卷(苏教版2019必修第一册)上海市黄浦区2021届高三三模数学试题北京市海淀区2020-2021学年高二下学期数学期中试题(已下线)数学-2022年高考押题预测卷03(北京卷)辽宁省实验中学北校区2023-2024学年高二下学期期中测试数学试题
解题方法
3 . 已知数列
的前n项和为
,满足
.
(1)求证:
是等差数列;
(2)已知
是公比为q的等比数列,
,
,记
为数列
的前n项和.
①若
(
是大于2的正整数),求证:
;
②若
(i是某个正整数),求证:q是整数,且数列
中的每一项都是数列
中的项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25673902449184f5727cbc786aa82a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd56c886d76991ec450d4aa1b7a6174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5274adf9ab52f082fb4f8f557e701621.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25673902449184f5727cbc786aa82a0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf92b5d061e45e1c720cdf93409ae75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd95636852e2bc9a178e2e9c012175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faab43e42c933f4a72763ff298844db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee956329e95a172d86c86b2f6af7aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd4f7a23f369403dea2892fee983c69.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac52d20d7bb3a6631f5035ef18b64c19.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
名校
解题方法
4 . 已知数列
满足
,
,
.
(1)若
,
,
,求
的取值范围;
(2)若
是公比为
的等比数列,
,
,
,求
的取值范围;
(3)若
成等差数列,且
,求正整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcc6ce3e2e0bb830573be30367749ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55b58f3f154dc5acafe10e3878cacb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3859890e300f470dcf4a215249da07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2efba990f1fca3fe00fb5e0a7fff0bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519dd3429eb0baf2355bfed8fd17426d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dd42e4f493477fb0f36137893d4d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9fa4aae0312cf88c6448033869a9261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
5 . 已知数列
是等比数列,且
,
,数列
满足:对于任意
,有
.
(1)求数列
的通项公式;
(2)若数列
满足:
,
,设
,当且仅当
时,
取得最大值,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135c20407aa59f589f9e2e837fc37b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea72f0e6d6599c25850647bdef96ec2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79560cd442650b675d08e9ca65856685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37115bee81c499659e8a110f907535b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894079e90dbd238139e7c0a65239a66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
6 . 设等差数列
的公差为
前
项和为
且
则
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814d72e9996cb40000585f8ce6695a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117464f527849ab995858aaa20f4175b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e73352584cdf17623292107a4dd990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01943ddfc6733cc24442ede2231f6c9.png)
您最近一年使用:0次
2019-11-04更新
|
1092次组卷
|
4卷引用:江西省宜春市铜鼓中学2020-2021学年高一(实验班)下学期第一次月考数学(理)试题
江西省宜春市铜鼓中学2020-2021学年高一(实验班)下学期第一次月考数学(理)试题上海市南洋模范中学2018-2019学年高三下学期开学考试数学试题(已下线)考向20 简单的线性规划-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-1
14-15高三上·山东济南·期末
名校
解题方法
7 . 设数列
的前n项和为
,已知
,
,数列
是公差为
的等差数列,n∈N*.
(1)求
的值;
(2)求数列
的通项公式;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f429bbac93a7e98eaf10f7a396e3626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67422ec81eb7f58bded010a3f20ff2e.png)
您最近一年使用:0次
2016-12-03更新
|
1705次组卷
|
5卷引用:江西省宜春市铜鼓中学2020-2021学年高一(实验班)下学期第一次月考数学(理)试题
江西省宜春市铜鼓中学2020-2021学年高一(实验班)下学期第一次月考数学(理)试题(已下线)2014届山东济南外国语学校高三上学期质量检测理数学试卷【全国校级联考】江苏省溧水第二高级中学等七校2017-2018学年高二下学期期联考数学试题江苏省南京市秦淮中学2017-2018学年高二下学期期中考试数学试题(已下线)专题10 数列通项公式的求法 微点3 累乘法