名校
解题方法
1 . 如果一个数列从第
项起,每一项与它得前一项得差都大于
,则称这个数列为“
”数列.
(1)若数列
为“
数列”,且
,
,
,求实数
的取值范围;
(2)是否存在首项为
的等差数列
为“
数列”,且其前
项和
满足
?若存在,请求出
的通项公式;若不存在,请说明理由;
(3)已知等比数列
的每一项均为正整数,且
为“
数列”,
,
,当数列
不是“
数列”时,试判断数列
是否为“
数列”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129d17c9a49272d44a0e70346414d12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129d17c9a49272d44a0e70346414d12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f73a97d20f5bc6ce114cd7ae7845c009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b1bfb98c2ca5473a25db8e422aa3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f89df42fedf7bee8a1756c7e4b7488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)是否存在首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9862c3f79df375b515dc9f707c763444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.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/a041c7a8d92b961e1d401ec7729b0e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(3)已知等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16a90364bdffdb10175942d399cc895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c22fc9b4692629ca685f0db29c9837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
您最近一年使用:0次
名校
解题方法
2 . 若定义在
上的函数
满足:对于任意实数
,总有
恒成立,我们称
为“类余弦型”函数.
(1)已知
为“类余弦型”,且
,求
和
的值;
(2)在(1)的条件下,定义数列
(
),求
的值;
(3)若
为“类余弦型”,且对任意非零实数
,总有
,证明:
①函数
为偶函数;
②设有理数
满足
,判断
和
的大小关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146ff57d46a7f258604e9660a726fdba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5459c2261022c328d84056a6a8e4e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365f5ac9c0d75ff80bd10f9924cfdd80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c228ab4a1edb2af494ff1d7c898518.png)
(2)在(1)的条件下,定义数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa8f9855ba25451049aa4630023e6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4a303c19edd204b3909c79c9a7632a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2316f10f32fb86134073f413f7a7b14.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d75465362a8dc41f4c3155ecb63f17.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②设有理数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a0b534b683b7e7210a261211af142a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915b3d29d0c7dd83c188e3ce31f52fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a4bf4bb3622d9396a2d975e96558a2.png)
您最近一年使用:0次
3 . 对任意正整数
,
,定义函数
如下:
①
;
②
;
③
.
(1)求
的解析式;
(2)设
是自然对数的底数,
,
,比较
与
的大小.
![](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/1e058f4325169eafcc30081eaf45327a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4083bd347f947ac13e6c177ade147c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2514dc16490d7266ab90eb686f7f1011.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3e9fe7e0e1dd0e736ed8c78824505e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ddb5e9c3a2b64ae846db75d0643c72.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45845a0b2b4bfb0a0f0845098c063b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f8771af38d3d6ba30daea296372c6c.png)
您最近一年使用:0次
4 . 对于无穷数列
、
,
,若
,
,则称数列
是数列
的“收缩数列”,其中
、
分别表示
中的最大项和最小项.已知数列
的前
项和为
,数列
是数列
的“收缩数列”.
(Ⅰ)写出数列
的“收缩数列”;
(Ⅱ)证明:数列
的“收缩数列”仍是
;
(Ⅲ)若
,求所有满足该条件的数列
.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4b279f31a9ebd5d03ee171e7134a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8424af9108fc00fbf86a3d5c9409e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689a822a0d8b276fbe8596a2f94f7022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dd42e4f493477fb0f36137893d4d06.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅰ)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dee512e0fdb19fc03858ce717ce8b7.png)
(Ⅱ)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c1201efe37bb0f8db97f93459d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2021-05-29更新
|
809次组卷
|
2卷引用:北京市第八十中学2021届高三考前练习数学试题
5 . 若数列
满足“对任意正整数
,
,
,都存在正整数
,使得
”,则称数列
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
的无穷等比数列
具有“性质
”,求首项
的值;
(3)若首项
的无穷等差数列
具有“性质
”,求公差
的值.
![](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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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)若首项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](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/5c02bc0c74292b1e8f395f90935d3174.png)
您最近一年使用:0次
2021-05-10更新
|
598次组卷
|
2卷引用:上海市虹口区2021届高三二模数学试题
6 . 已知各项均为整数的数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad107fc0e55e4b35b2b25b10f75f4e6.png)
.满足
,且对任意
,都有
.记
.
(1)若
,写出一个符合要求的
;
(2)证明:数列
中存在
使得
;
(3)若
是
的整数倍,证明:数列
中存在
使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad107fc0e55e4b35b2b25b10f75f4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0ed3f2a79403d4ca1cf2f9def5ae31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e557ad17fa38ac6b1f55e6ad6ec3c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c906536bb830afee02111d791983e06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b389b37b65b78e0242245f67b5f2dc82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6735b270c7b4dbf195e1834d745e3dd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f762938f5c78eb72bafbb13bf85cba1.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818b44478f6d1d972aa5bf6dd4d3a0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433eaf536c1fed0f48f4af7b595a2af4.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d76da8e15e302756b4d2e7e24906ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818b44478f6d1d972aa5bf6dd4d3a0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5566b1d828acdac47fe50216d247cfac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cc91f55eeaa0330a9586ee73912466.png)
您最近一年使用:0次
2021-05-07更新
|
1196次组卷
|
9卷引用:北京市朝阳区2021届高三下学期二模数学试题
北京市朝阳区2021届高三下学期二模数学试题北京市朝阳区人大附中朝阳分校2022届高三12月月考数学试题北京市第八中学2021-2022学年高二6月月考数学试题北京市第二中学2023届高三上学期10月月考数学试题北京市第五十七中学2023届高三上学期12月月考数学试题北京市北京理工大学附属中学2023届高三下学期开学测试数学试题北京市第五中学2022-2023学年高二下学期期末检测数学试题【北京专用】专题03数列(第三部分)-高二上学期名校期末好题汇编(已下线)专题01 数列(6大考点经典基础练+优选提升练)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)
解题方法
7 . 定义:符号
表示实数
、
、
中最大的一个数;
表示
、
、
中最小的一个数. 如,
,
.设
是一个给定的正整数
,数列
共有
项,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01199da4114511b6f3dced0fa4c50426.png)
,
.由
的取值情况,我们可以得出一些有趣的结论.比如,若
,则
.理由:
,则
.又
,
,于是,有
.试解答下列问题:
(1)若数列
的通项公式为
,求数列
的通项公式;
(2)若数列
满足
,
,求通项公式
;
(3)试构造项数为
的数列
,满足
,其中
是等比数列,
是公差不为零的等差数列,且数列
是单调递减数列,并说明理由.(答案不唯一)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225be414d59a022c9456348f56784318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d669c05de69c4e82327576e630e690de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd3c167e5fb2a5de897cbfededb1c75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d375f8080f4f9297d079a1556211118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d09f994198167ee71a261a20e437eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01199da4114511b6f3dced0fa4c50426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01042971eb25362b7a3f1c0643c4670d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658c3b3e72ac3a53632210c0c3de3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50a4b1e4f8b1d044300df7ef8205c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974ec2ba8cc5c3359a112eb7eef246a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5083a59d00ee26f5709202fa5344630c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974ec2ba8cc5c3359a112eb7eef246a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc35a1a6558499dbf8e368682bf46f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46148262daa2e1b3ef29f08701702c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e6b55263081a4c048677e232213189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5083a59d00ee26f5709202fa5344630c.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a6590a4909d70cbf8ed3e58e4978da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26219cb164d1ef457ce21fdf99376e5f.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3af24e0787167e622c0375b7a279a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d07b502d14c9431029a0645fa04cbca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)试构造项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb2db37e079b735acc41ea3035139e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35d2715b9e36e8bb1b69d2f9fadb358.png)
您最近一年使用:0次
8 . 已知无穷数列{an},对于m∈N*,若{an}同时满足以下三个条件,则称数列{an}具有性质P(m).
条件①:an>0(n=1,2,…);
条件②:存在常数T>0,使得an≤T(n=1,2,…);
条件③:an+an+1=man+2(n=1,2,…).
(1)若an=5+4![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
(n=1,2,…),且数列{an}具有性质P(m),直接写出m的值和一个T的值;
(2)是否存在具有性质P(1)的数列{an}?若存在,求数列{an}的通项公式;若不存在,说明理由;
(3)设数列{an}具有性质P(m),且各项均为正整数,求数列{an}的通项公式.
条件①:an>0(n=1,2,…);
条件②:存在常数T>0,使得an≤T(n=1,2,…);
条件③:an+an+1=man+2(n=1,2,…).
(1)若an=5+4
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cba79639deae5f8af6088b30c1a800.png)
(2)是否存在具有性质P(1)的数列{an}?若存在,求数列{an}的通项公式;若不存在,说明理由;
(3)设数列{an}具有性质P(m),且各项均为正整数,求数列{an}的通项公式.
您最近一年使用:0次
2021-05-02更新
|
1166次组卷
|
5卷引用:北京市海淀区2021届高三下学期期中数学试题
9 . 已知数列
,具有性质P:对任意
(
)
与
,两数中至少有一个是该数列中的一项,
为数列
的前
项和.
(1)分别判断数列0,1,3,5与数列0,2,4,6是否具有性质P:
(2)证明:
且
;
(3)证明:当
时,
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab0618ddda6e7eeba8a14c2655833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb18c6dbf63138dd5cf7cae946c106e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae331839bce8f3c14d7efd7f9d8915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)分别判断数列0,1,3,5与数列0,2,4,6是否具有性质P:
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1fe4c51169a32e05e4be4acb3d1f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc31cec2f263c4fbed39962f960daef.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd49c085be2656091b79da53f010a1a.png)
您最近一年使用:0次
2021-03-25更新
|
947次组卷
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3卷引用:北京平谷区2021届高三数学一模试题
名校
10 . 已知函数
.
(1)讨论f(x)的单调性;
(2)设
.
(i)证明:
是递减数列;
(ii)已知集合
,求A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28585cdf1037ab924cad4b6c27831965.png)
(1)讨论f(x)的单调性;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77fb95e03409e01911e834ac8e757d0.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(ii)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3bc98ffc7aa55aa7ab2b60f86dc37c.png)
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