设正整数集合
,且
.若对于任意的
,当
时,都有
,则称集合 A 为“子列封闭集合”.
(1)若
,判断集合 A 是否为“子列封闭集合”,说明理由;
(2)若数列
的最大项为
,且
,证明:集合 A 不是“子列封闭集合”;
(3)设
为数列
,若
,且集合 A 为“子列封闭集合”,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd97a983f9ea1b4d42a014f74b78043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f132a0562b4f6a16463b6611e655f827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0cb17e62b4bb00f14dfcb01741ccb30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6498d760af8e823bab06cf73d1b35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482d33ab769aa9f133101de842ad1156.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f61344f46c3a45f2dd826bb94d3de4.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea00d10c496ccacb5b25c9574d6cdb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba583497b12122c6e037eeffe602008.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48d518b037dc02314fab2d544b87d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9c5f0e9efe7c63a8f37072aa0a0e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
更新时间:2023-05-19 09:26:32
|
相似题推荐
【推荐1】物理学家牛顿用“作切线”的方法求函数零点时,给出了“牛顿数列”,它在航空航天中应用非常广泛.其定义是:对于函数
,若满足
,则称数列
为牛顿数列.已知
,如图,在横坐标为
的点处作
的切线,切线与x轴交点的横坐标为
,用
代替
重复上述过程得到
,一直下去,得到数列
.
的通项公式;
(2)若数列
的前n项和为
,且对任意的
,满足
,求整数
的最小值.(参考数据:
,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac875e4401d9d0a697586cca8871f32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044fd1cba45366a7c3064637f469bdb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17fee5467d57f0978ea70d4648a7217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1505d56f0b35fe7f2de1fe1888036e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cca0ad4934d67935c9207cd12dc5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0848b0f826a63fea6286d2c52b18c549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539ae63efa6aab52e5b6a4190c684ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e3b17aa93b9ff98c93f7d097b8c38d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a5e288e8c07edfb9ad3c5f0f322fcc.png)
您最近一年使用:0次
【推荐2】已知数列
中
,
(
).
(1)求数列
的通项公式
及前
项和
;
(2)(此问题仅理科作答)设
,求证:
.
(此问题仅文科作答)设
, 求数列
的最大项和最小项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53dbdc7656747b4fdfbc24dd4a951038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856066bd1a819be18ad817e015f7fb6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)(此问题仅理科作答)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefb3d15a3d45cdf54f99ec0c9516280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c322010ba1d686d52fd79d1cb78a71ee.png)
(此问题仅文科作答)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf8c5e743efa6987f5463abfa9c2db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f88b0a97a3e7187e9f048c0c3ba147.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
【推荐1】设数列
.定义集合
,
,其中
为给的正整数.
(1)若
,求
;
(2)若
中的项
,求证:
为常数列;
(3)记集合
的最大元素为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cef122118d272825a7bc8c336f1bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f4ab40307da20dd6a011ef33c51b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b8909e1435bc70e6f209b2df94de88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd8aecb16302a7973a6d4eb86c3cc6e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd2c56d022774693603879f37b5dc27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1435ac5c72edbdf99c02c6354870e4d3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49571ac4685f51e68bab0b282dbd0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd62c987ebd28ec20e8d59d1a3b02c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520a8a20577ce2f7aa9533516b80dead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970aca8f11113fa58bc11998a5ed0b1b.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
【推荐2】对于数列
,记
,
,
,则称数列
为数列
的“
阶数列”.
(I)已知
,若
为等比数列,求
的值;
(II)已知
,若
,且
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31f66a3ec17a0558ef2baf352cc2ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43bc713ddd3aa6a74897bbcaab667f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb0f156c3f4f018057df27e00b6c5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6407a3c218d72a003ff101d24adf608f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(I)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc24b4655c93d7bbc2b30f890ad25e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(II)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3770498c81d0241e0f6d7f1019fe6d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e4fd5f895fff36791fa106911037db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
您最近一年使用:0次