名校
解题方法
1 . 数列
:
,
,…,
满足:
,
,
或1(
,2,…,
),对任意i,j,都存在s,t,使得
,其中
且两两不相等.
(1)若
,直接写出下列三个数列中所有符合题目条件的数列的序号:
①1,1,1,2,2,2;②1,1,1,1,2,2,2,2;③1,1,1,1,1,2,2,2,2
(2)记
,若
,证明:
;
(3)若
,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.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/d8dc3192c861a4cc44da88f656ae7aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564e60383b05d2e0ee94a733742ae424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631c6879b8799ed0f1aefbf28bf988f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c4d0383577207858e39b4b19b0853e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631c70b687b22d032d1cc5050cfc07dc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
①1,1,1,2,2,2;②1,1,1,1,2,2,2,2;③1,1,1,1,1,2,2,2,2
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb1eff85b93cd753c2a3a4fb9603221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743b4f6fde34464397b010cb45eabb7d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afa6e51b3b27c3edb330cd7f190b6cf.png)
您最近一年使用:0次
2023-08-05更新
|
742次组卷
|
5卷引用:北京市海淀区清华大学附属中学2022-2023学年高二上学期期中考试数学试题
名校
2 . 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
的子列.
注:从
中选取第
项、第
项、…、第
项(
)形成的新数列
称为
的一个子列.
(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
的值;
(3)求证
.
![](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/6ae8297742318e91be10074c89f212bc.png)
条件②:从集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8297742318e91be10074c89f212bc.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/68c6d8698bc7a9af6c0e9e2b7fb8b240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02034a7c04920a212f7974cd64dde9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823953737f36a700af348506ee8c678b.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/2dc0c923d538857536c1d74635147369.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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c118e992e32545ff658a95c284165cd.png)
(3)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db133f4329ff1231e7cd04148651d48b.png)
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2023-08-02更新
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2卷引用:北京市清华附中2022-2023学年高二下学期期末数学试题
3 . 设
为无穷数列,给定正整数
,如果对于任意
,都有
,则称数列
具有性质
.
(1)判断下列两个数列是否具有性质
;(结论不需要证明)
①等差数列
:5,3,1,…;②等比数列
:1,2,4,….
(2)已知数列
具有性质
,
,
,且由该数列所有项组成的集合
,求
的通项公式;
(3)若既具有性质
又具有性质
的数列
一定是等差数列,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8feaf51b5fdc0b7aad38b26f57825712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575e42a3bdb429360418e949bd963a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
(1)判断下列两个数列是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
①等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f3e9d115d6290eee217a29dc399cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若既具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee83304e529e6d24ea7ff894bd6d87a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-07-10更新
|
813次组卷
|
5卷引用:北京市西城区2022-2023学年高二下学期期末考试数学试题
北京市西城区2022-2023学年高二下学期期末考试数学试题(已下线)高二数学下学期期末押题试卷01【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02 等比数列4种常考题型归类【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(北京专用)(已下线)2024年新课标全国Ⅰ卷数学真题变式题16-19
4 . 已知数列
的项数均为m
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34919e3b413417f8fcc06fbfbca9bfe0.png)
的前n项和分别为
,并规定
.对于
,定义
,其中,
表示数集M中最大的数.
(1)若
,求
的值;
(2)若
,且
,求
;
(3)证明:存在
,满足
使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53fc8ddaa412b237ecb095cf1c65335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34919e3b413417f8fcc06fbfbca9bfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b64f109cde567dc5750276a16a6b774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d230d1915653fb876373f882ca81b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd13665a47f5548727c599936b32dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2d6df455d7702a81bdbc86f17e8c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698f45c9ed5bb04924f1037107e76988.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc21f6a796961cc506633a4fe32563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd374d21bbdff3c6f8e69b557a86e2ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295f2712a68800672db5c617713eedf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9de2f1a28584f093949cc0b854dfb3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135cb036833400f3fa1edc92d5ce410.png)
(3)证明:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23a3f55b2eb456a65b9788574437678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363d7ed2c067c37fb1dfc5e2a50ba573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eedada19441233cfac2f4e4322cf85.png)
您最近一年使用:0次
2023-06-19更新
|
10560次组卷
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19卷引用:专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)
(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)2023年北京高考数学真题专题05数列(成品)(已下线)2023年北京高考数学真题变式题16-21北京十年真题专题06数列北京市丰台区第二中学2024届高三上学期开学考数学试题北京市第八十中学2023-2024学年高三上学期10月月考数学试卷(已下线)数列新定义(已下线)专题6.1 等差数列及其前n项和【九大题型】(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)专题30 等比数列通项与前n项和(已下线)专题21 数列解答题(理科)-2(已下线)专题21 数列解答题(文科)-3(已下线)专题2 考前押题大猜想6-10专题06数列专题14数列(已下线)五年北京专题10数列(已下线)三年北京专题10数列
5 . 设数列
,即当
时,
.记
.
(1)写出
,
,
,
;
(2)令
,求数列
的通项公式;
(3)对于
,定义集合
,求集合
中元素的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa7b3c190459af645f8bfb2d287fcde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808d924a0869b4fd83c2af3a9c08c755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21d7086ab24e85a3a109596d2112065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48990b6e63ba2d3697523faab15d4846.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2714e51cd5b5f0529bcad6499c1b9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
(3)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b04dd5926d27d2fe7c375030018df26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0720f874c2f8b28c8c289dddb362f336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d88909e5fcc68bc96d756f2d65060c.png)
您最近一年使用:0次
名校
解题方法
6 . 已知
是由非负整数组成的无穷数列.该数列前
项的最大值记为
,第
项之后各项
的最小值记为
,
.
(1)若
为
,是一个周期为
的数列(即对任意
,
),写出
,
,
,
的值;
(2)设d是非负整数.证明:
(
)的充分必要条件为
是公差为d的等差数列;
(3)证明:若
,
(
),则
的项只能是
或者
,且有无穷多项为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36c4148c78af85e5c41562480a84fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b009b18d73c19e79a6d6d6650e309b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b623b0c3e8607f3442c87c4ac4014c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517a9ba04901f83049080e17e971ba7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a4cfdd9e07678b0f956f89b287b953.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36c4148c78af85e5c41562480a84fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373ca638ab28d1698d0ca2a5a5b9824e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8592a1051a0927bd54d00e26d319553f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42eeef885805aa18e46cf9725c0e3248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a8d81f40b67ff5d714187185b7fdee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c3825613df085d82ffdb03ede72b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dba9c413d5c2589337d1c70c2d3e456.png)
(2)设d是非负整数.证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8c61017b023911c75e4d404b4785cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bce6187f3f11e0ceead8a645f5f9d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9847d6f5934b3b18db97298dd4f83c97.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f9dc35e423accb60225ee1d062d33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f99489791db717b082bd96abb88c55e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469e197b1ba72e5d014def3a4b1fc946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1007a9a47e18a607d487a4d4a9559a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
7 . 给定项数为
的数列
,其中
.若存在一个正整数
,若数列
中存在连续的
项和该数列中另一个连续的
项恰好按次序对应相等,则称数列
是“
阶可重复数列”,例如数列
.因为
与
按次序对应相等,所以数列
是“4阶可重复数列”.
(1)分别判断下列数列
①
.
②
.
是否是“5阶可重复数列”?如果是,请写出重复的这5项;
(2)若项数为
的数列
一定是“3阶可重复数列”,则
的最小值是多少?说明理由;
(3)假设数列
不是“5阶可重复数列”,若在其最后一项
后再添加一项0或1,均可使新数列是“5阶可重复数列”,且
,求数列
的最后一项
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9020dc88b1accc2081b709d3223dbbc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a71274da41000756972672ffafdf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0d72cc445f8f338f8c1a629576d36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a271ffc03fc4d7f80a5c972a344bc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee46e364b6de2aed96c320afa237da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)分别判断下列数列
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf667803a56ccb07f8ba2e3e27173b12.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ef60c1bd9077b7e57b039d5600718d.png)
是否是“5阶可重复数列”?如果是,请写出重复的这5项;
(2)若项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)假设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2da0ff9dc73d62f8162fc3de186150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
您最近一年使用:0次
名校
解题方法
8 . 在无穷数列
中,
,对于任意
,都有
,
.设
,记使得
成立的n的最大值为
.
(1)设数列
为
,写出
,
,
,
的值;
(2)若
为等差数列,求出所有可能的数列
;
(3)设
,
,求
的值.(用p,q,A表示)
![](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/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b270a87d8e670809520e33c85bc3899a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f29c06a3e9a73e905eb87d71efa201c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19db2869aeaf97debfa2e2f9a4843a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2e9fa110dfaaeb7105910008e0551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e2d10a44a59e7f9f040c1750611855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153dea9219e2e63af7bf504f2bba2d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1069c8dcd25a6f743a758606bd296d7.png)
您最近一年使用:0次
2023-05-05更新
|
496次组卷
|
3卷引用:北京市一零一中学2022-2023学年高二下学期期中考试数学试题
北京市一零一中学2022-2023学年高二下学期期中考试数学试题北京市海淀区北京一零一中2023-2024学年高二下学期期中考试数学试题(已下线)北京市第四中学2024届高三上学期10月月考数学试题变式题16-21
9 . 设
为整数.有穷数列
的各项均为正整数,其项数为m(
).若
满足如下两个性质,则称
为
数列:①
,且
;②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4daddea99be0888d1d6c560987c4bc2.png)
(1)若
为
数列,且
,求m;
(2)若
为
数列,求
的所有可能值;
(3)若对任意的
数列
,均有
,求d的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.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/280f1e7d3e287061e928c064f2197e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7577a0af23649b4a2a25326fb9499c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b02eaacb42cc64295856fefdd5d287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4daddea99be0888d1d6c560987c4bc2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c39770fd747beb3f0431bd6e86876e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43703b905a9846c8f49f23b07ca661d.png)
您最近一年使用:0次
2023-05-05更新
|
1851次组卷
|
6卷引用:专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)北京市海淀区2023届高三二模数学试题北京卷专题18数列(解答题)(已下线)专题15 数列不等式的证明 微点1 反证法证明数列不等式北京市朝阳区2024届高三上学期数学期中模拟数学试题江苏省南京市南京外国语学校2024届高三下学期2月开学期初考试数学试题
名校
10 . 已知数列是由正实数组成的无穷数列,满足
,
,
,
.
(1)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)判断:是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7306bacb80799eeabd3fd46cb8632598.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.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/74828c0bbc29e16c346941b7d4287f2f.png)
您最近一年使用:0次
2023-04-06更新
|
1207次组卷
|
6卷引用:上海外国语大学闵行外国语中学2023-2024学年高二上学期期中数学试题
上海外国语大学闵行外国语中学2023-2024学年高二上学期期中数学试题上海市杨浦区2023届高三二模数学试题(已下线)专题06 数列及其应用北京市海淀区2023届高三数学查缺补漏题(2)(已下线)北京市第四中学2024届高三上学期10月月考数学试题变式题16-21重庆市九龙坡区育才中学校2024届高三下学期阶段测试数学试题