若无穷数列
满足:只要
,必有
,则称
具有性质
.
(1)若
具有性质
,且
,求
;
(2)若无穷数列
是等差数列,无穷数列
是公比为正数的等比数列,
,
,判断
是否具有性质
,并说明理由;
(3)设
是无穷数列,已知
,求证:“对任意
都具有性质
”的充要条件为“
是常数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3485725c313650a3112c7f7af6898f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c0b488096f27c73fc960e27f3b864a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878286bfd63b2d13de2f21cd143ec9fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf8005bbae305249bf1193471fa7064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51fe5ae3b4696e24316810e043cffc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26d073deea51822ecd1a965655d20ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee22f915281b048adfaa8b566e40d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
更新时间:2020-12-01 19:57:29
|
相似题推荐
解答题-证明题
|
较难
(0.4)
名校
解题方法
【推荐1】已知集合
中含有三个元素
,同时满足①
;②
;③
为偶数,那么称集合
具有性质
.已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2472afe9a850dd4ed6e2d5f0dc986ec9.png)
,对于集合
的非空子集
,若
中存在三个互不相同的元素
,使得
均属于
,则称集合
是集合
的“期待子集”.
(1)试判断集合
是否具有性质
,并说明理由;
(2)若集合
具有性质
,证明:集合
是集合
的“期待子集”;
(3)证明:集合
具有性质
的充要条件是集合
是集合
的“期待子集”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d561cdf17d3a6d7d57af719cb6100c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55de080a3c1313bbd6ea5c17307c723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2472afe9a850dd4ed6e2d5f0dc986ec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bccfdca384d27d0d8395068e21770157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60809c809060f8d3f7a2d13b4baf6cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)试判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f640ba418f74a232666dc3fb3abfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff95c388d22eba3d62c196277b47a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
(3)证明:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐2】已知数列
的各项均为正数,
是数列
的前n项和,记
,
.
(1)若
是等差数列,且
,
,求
;
(2)若
,
,且对任意
,
,
,
成等差数列,求数列
的通项公式;
(3)证明“对任意
,
,
,
成等比数列”的充分必要条件是“对任意的
,数列
,
,…,
成等比数列”.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9a19f94917dde4a021b8e8f75ea06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6fc3f281738019c3f756be1d4ea563.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139aefc2be29ebedf8b3d1a12faf8065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4657f5632b5e2f7f89c5723f33c22d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c752ebe8516e7d3327f3410473d9a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62e1e08999624092770dcb758089f81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15526f7c892333030073b85fc3baee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)证明“对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15526f7c892333030073b85fc3baee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.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/e3d8af4e2b2c48c73e7897eb3da814c8.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
名校
【推荐1】给定正整数k,m,其中
,如果有限数列
同时满足下列两个条件,则称
为
数列.记
数列的项数的最小值为
.
条件①:
的每一项都属于集合
;
条件②:从集合
中任取m个不同的数排成一列,得到的数列都是
的子数列.
注:从
中选取第
项、第
项、…、第
项(其中
)形成的新数列
称为
的一个子数列.
(1)分别判断下面两个数列是否为
数列,并说明理由:
数列
;
数列
;
(2)求证:
;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff8f43f54aaab94d126c2ed7c929196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33bf403c186b3c6747b2d9d1dd75990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33bf403c186b3c6747b2d9d1dd75990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733309155391786ce67cf7becf69cfdc.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397303cf4747941d4e68c649168308b9.png)
条件②:从集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397303cf4747941d4e68c649168308b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
注:从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5f59bc23cf55f56312c9ed9806371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af9e7b1c23db5584ad8521d4444d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749cd20d9be1925f0d1d7aa4b3660308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1ede9d1caaf88f47e9ab027394b4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03747bd03d463752a44ad2396506e93f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)分别判断下面两个数列是否为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b218eb05c837c471564a8de0a8df01e3.png)
数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8f0c365d19e8120876cd2dcc22f215.png)
数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa0ced8f2185d0f51a3b44cc247d302.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6cae7fcca373eb22a7e1e4cb336418.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a740d8b3e5fd2e09cad35ea37f623d5e.png)
您最近一年使用:0次
【推荐2】设p为实数.若无穷数列满足如下三个性质,则称
为
数列:
①,且
;
②;
③,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be16c2cf7aae777e1b68354fe0b3543.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9d7c2eeebbf6d24c659dec05e7cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(3)设数列
![](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/b46cd00743394b0f8636c08fc6abc521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1391b1323ca839ae8bcc075f9387935f.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
解题方法
【推荐3】给定一个
项的实数列
,
,
,
,任意选取一个实数
,变换
将数列
,
,
,
变换为数列
,
,
,
,再将得到的数列继续实施这样的变换,这样的变换可以连续进行多次,并且每次所选择的实数
可以不相同,第
次变换记为
,其中
为第
次变换时所选择的实数.如果通过
次变换后,数列中的各项均为
,则称
,
,
,
为“
次归零变换”.
(1)对数列
,
,
,
,给出一个“
次归零变换”,其中
.
(2)对数列
,
,
,
,
,给出一个“
次归零变换”,其中
.
(3)证明:对任意
项的实数列,都存在“
次归零变换”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/e6a449c0e8cc443f7858d2b649e1b664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e5927e6b179a7df32697f18ba04b41.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25131a07a6a031a124926266d5aaa88b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b372d905bbe18bf8d2ec74c036ba07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e727a8e24d83d3b25ab0f62185029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519200ff8ebddb67a64c4a2227069ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5925987d5a6eb1ce1fec68b810cb6fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ee29df273de449b10a025426080d05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a27d8a9d5cb3cbec59748cfa17107d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5925987d5a6eb1ce1fec68b810cb6fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54705e63ac8bd8e04bed5e81f476a35a.png)
(2)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ef963f7042f5648acebc2f38246f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7073684723741238b95b3b9d3b5301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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