名校
1 . 已知
是无穷数列,
,
,且对于
中任意两项
,
,在
中都存在一项
,使得
.
(1)若
,
,求
;
(2)若
,求证:数列
中有无穷多项为0;
(3)若
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55ef34345210312db273ab4981c40f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0616dca5cf0229b9f801365cc2bcfff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba50a82a53f0e597c096ccf5746f1b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53abaaac2e62f510d996e6db22aefe7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.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
2 . 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
名校
3 . 已知无穷数列
满足
,其中
表示x,y中最大的数,
表示x,y中最小的数.
(1)当
,
时,写出
的所有可能值;
(2)若数列
中的项存在最大值,证明:0为数列
中的项;
(3)若
,是否存在正实数M,使得对任意的正整数n,都有
?如果存在,写出一个满足条件的M;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba6d5fdf4c491c1332483be3cfab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37f161c1dd788025cef9910858df7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c03a27be8ae82e24b86cc52a92204c28.png)
(1)当
![](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/daf464629fa321a6ff7401ab79f07083.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a65d8762e567f485f39f81564b593a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
您最近一年使用:0次
2023-05-05更新
|
3807次组卷
|
19卷引用:北京市朝阳区2023届高三二模数学试题
北京市朝阳区2023届高三二模数学试题北京卷专题18数列(解答题)北京一零一中学2024届高三上学期统考一数学试题北京市景山学校2024届高三上学期10月月考数学试题(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(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北京市东城区东直门中学2024届高三上学期期中数学试题北京市海淀实验中学2024届高三上学期10月月考数学试题(已下线)专题01 条件开放型【练】【北京版】2024年全国普通高中九省联考仿真模拟数学试题(二)(已下线)高三数学开学摸底考02(新考法,新高考七省地区专用)(已下线)【一题多变】取大取小 分类讨论广东省2024届高三数学新改革适应性训练二(九省联考题型)(已下线)数列新定义北京市第二中学2023-2024学年高三下学期开学考试数学试卷(已下线)(新高考新结构)2024年高考数学模拟卷(二)上海市杨浦区复旦大学附属中学2024届高三下学期3月月考数学试题北京市顺义区第九中学2023-2024学年高三下学期3月月考数学试题广东省云浮市云安区云安中学2024届高三下学期3月模拟考试数学试题
名校
4 . 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:上海市杨浦区2023届高三二模数学试题
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
名校
解题方法
5 . 已知数列
中,
,且
,若存在正整数
,使得
成立,则实数
的取值范围为( )
![](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/53ca2cae224aae175d07a96cf95c9118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551b1fb748642c8e6b3deced91340b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-02-09更新
|
1152次组卷
|
2卷引用:福建省莆田市莆田第一中学2024届高三上学期第一次调研数学试题
6 . 已知
为正整数数列,满足
.记
.定义A的伴随数列
如下:
①
;
②
,其中
.
(1)若数列A:4,3,2,1,直接写出相应的伴随数列
;
(2)当
时,若
,求证:
;
(3)当
时,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97559b8ae5f9544c7b93bf2f9d03394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6559598727fb120a5cdbf4f15510615d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c995ba5a9caa036977b023f57a4202f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271c5044aeaf0fd2a6f75746754565c8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880b1efd3798a3ccf2633252b10e0ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570d7b5b193a644beb91889bbde27cde.png)
(1)若数列A:4,3,2,1,直接写出相应的伴随数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3053e2b8a6bbc35527a1e4505b84ed0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2578cb9428c41fa9236c6350bae49f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941e10d4febad08273c2b181023f019f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2578cb9428c41fa9236c6350bae49f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fac29b7c846a7ba3b612b0f7ebee41.png)
您最近一年使用:0次
2023-01-12更新
|
955次组卷
|
4卷引用:北京市顺义区2023届高三上学期期末考试数学试题
名校
7 . 斐波那契,意大利数学家,其中斐波那契数列是其代表作之一,即数列
满足
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75322d762ff76c3d02691a55264a4a6f.png)
,则称数列
为斐波那契数列.已知数列
为斐波那契数列,数列
满足
,若数列
的前12项和为86,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685e016946719e3baecb299494db4677.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75322d762ff76c3d02691a55264a4a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bdd4ae3688aa83708e29ef86dbec23.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1da9ac604e7548471f3366f03c856f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685e016946719e3baecb299494db4677.png)
您最近一年使用:0次
2023-01-06更新
|
1140次组卷
|
10卷引用:江西省赣州市2023届高三上学期1月期末考试数学(理)试题
江西省赣州市2023届高三上学期1月期末考试数学(理)试题福建省福州格致中学2022-2023学年高二下学期期中考试数学试题(已下线)专题15 数列求和-2上海市复兴高级中学2023-2024学年高二上学期期中数学试题福建省宁德第一中学2020-2021学年高二上学期开学检测数学试题上海市宝山中学2023-2024学年高二上学期期终考试数学试题(已下线)【一题多变】斐波那契数列1(已下线)盲点4 斐波那契数列(已下线)【练】 专题8斐波那契数列(已下线)【讲】专题4 数列新定义问题
解题方法
8 . 已知无穷数列
满足:①
;②
(
;
;
).设
为
所能取到的最大值,并记数列
.
(1)若
,写出一个符合条件的数列A的通项公式;
(2)若
,求
的值;
(3)若
,求数列
的前100项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6b7c794c3329ca99a71eb07c4a7b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8d9def91c6734e75134ef49ba0418a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a21caee5b908cd571bf28d61be90aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228114fab3c07bc63978df7e2dc31953.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8faa0cc59f291d53f801546d5dabe6fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa5e5f1551d40f96a03ca6975e68f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d00457e8d086f28ea1b24bd880c9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297bc58fc87efa1f15d7eb9b5eb42260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fb6fbf69268bc82274bc7ff03010c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51cf6e2a57173496d722a325ffd16af.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e35c9a35017d2fdcd10f76b4a776419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879ed18e2aaf5ef408be9e6ac8d9e30a.png)
您最近一年使用:0次
2022-05-30更新
|
1423次组卷
|
5卷引用:北京卷专题18数列(解答题)
北京卷专题18数列(解答题)(已下线)专题11 数列前n项和的求法 微点8 分组法求和北京市东城区2022届高三下学期综合练习(三)数学试题(已下线)2022年新高考北京数学高考真题变式题13-15题(已下线)2022年新高考北京数学高考真题变式题19-21题
9 . 已知数列
中,
,若
,则下列结论中错误的是( )
![](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/d8a64aee90aed584681c3b924f8db03a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-05-26更新
|
1916次组卷
|
6卷引用:专题6-1 数列函数性质与不等式放缩(讲+练)-2
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2022·全国·模拟预测
10 . 已知数列
满足
,
,
,数列
的前n项和为
,且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640e40b1b87fdd9c8bee7c1a5bae78b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2adf14bea097284d798138dcb07b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cbac4858faac6c9ac77816d503ad46a.png)
A.![]() |
B.![]() |
C.数列![]() |
D.满足不等式![]() |
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