1 . 设
是正整数,如果存在非负整数
使得
,则称
是
好数,否则称
是
坏数.例如:
,所以2是
好数.
(1)分别判断
是否为
好数;
(2)若
是偶数且是
好数,求证:
是
好数,且
是
好数;
(3)求最少的
坏数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3e9eb0c4bd9c899886668229c4c947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f926787912ab3b608ab631821c5edb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bae21b1ed66af11d8e79fca68969ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbbe31b06cbf700d55a3b7b23b16c8ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2837786afdd7b9b8bc37823040d7dd64.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01922b842f6a0f56a49ddf6e02860e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4815b8b7203fb465809b395153ea3340.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0d553db3c201b986582e86c52d402b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c46af2ff5b39b2e20c17f15cbdf5ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
(3)求最少的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d261dc1ce8dcbd2bb899cf45837291b5.png)
您最近一年使用:0次
2 . 已知数列
,给出两个性质:
①对于任意的
,存在
,当
时,都有
成立;
②对于任意的
,存在
,当
时,都有
成立.
(1)已知数列
满足性质①,且
,
,试写出
的值;
(2)已知数列
的通项公式为
,证明:数列
满足性质①;
(3)若数列
满足性质①②,且当
时,同时满足性质①②的
存在且唯一.证明:数列
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
①对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63aba9ebaf75a7c786ead3acf592124f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7368220470ebd17a0fd2bcf1f9fd495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d69f0ac02c5f17f270441a9ec3415d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1894bb426f0b3c7571d2963dbdbe7a.png)
②对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851dfb39ca2a28a2f730f0b73e1f5371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7368220470ebd17a0fd2bcf1f9fd495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93ba943c3bb91003519ec6c2bfa999a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1894bb426f0b3c7571d2963dbdbe7a.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99cd38e2e49d36cda164915acc9c2e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0233e44eb75be4271f48362e028d9f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72572c302243a18a7840782a7813e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe43c6bbc58db0df3ddc90957f908748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e18aac23f83ed46b98a6421df6dd17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ffc3b6e643dec84faf0eeccab1b610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d0a2aa878c3c5b57e3609825b0d431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
您最近一年使用:0次
2022-05-11更新
|
803次组卷
|
4卷引用:北京卷专题18数列(解答题)
3 . 已知数列
的各项均为正整数,设集合
,
,记
的元素个数为
.
(1)若数列A:1,3,5,7,求集合
,并写出
的值;
(2)若
是递减数列,求证:“
”的充要条件是“
为等差数列”;
(3)已知数列
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f885247785940c5c849210fb6f8abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4884c506476f191d7919cd266c8c0212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a0c2bb484bf523189b093485eca999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(1)若数列A:1,3,5,7,求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3197c615558fee3993d2a8deb9091f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d509697c5391a7c24d9bbc2c82422b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff241fc46c23ac975c5b39e87a9e46a.png)
您最近一年使用:0次
2024-04-19更新
|
336次组卷
|
4卷引用:2024年北京高考数学真题平行卷(基础)
(已下线)2024年北京高考数学真题平行卷(基础)(已下线)集合与常用逻辑用语-综合测试卷B卷黑龙江省双鸭山市友谊县高级中学2024届高三下学期高考模拟(一)数学试题吉林省长春市长春吉大附中实验学校2023-2024学年高二下学期5月期中考试数学试卷
名校
解题方法
4 . 定义:若对任意正整数
,数列
的前
项和
都是整数的完全平方数,则称数列
为“完全平方数列”.
(1)若数列
满足
,判断
为是否为“完全平方数列”;
(2)若数列
的前
项和
(
是正整数),那么是否存在
,使数列
为“完全平方数列”?若存在,求出
的值;若不存在,请说明理由;
(3)试求出所有为“完全平方数列”的等差数列的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e95905e3f5d8dc67f74b44febb07353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8af66591a4140c35b3a9f01c9530d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ee9273cc82d57d99a21fb9c4953d46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)试求出所有为“完全平方数列”的等差数列的通项公式.
您最近一年使用:0次
2023-07-21更新
|
337次组卷
|
4卷引用:【北京专用】专题01数列(第一部分)-高二上学期名校期末好题汇编
【北京专用】专题01数列(第一部分)-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)北京市怀柔区2022-2023学年高二下学期期末考试数学试题江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题
解题方法
5 . 已知函数
,对于数列
,若
,则称
为函数
的“生成数列”,
为函数
的一个“源数列”.
(1)已知
为函数
的“生成数列”,
为函数
的“源数列”,求
;
(2)已知
为函数
的“源数列”,求证:对任意正整数
,均有
;
(3)已知
为函数
的“生成数列”,
为函数
的“源数列”,
与
的公共项按从小到大的顺序构成数列
,试问在数列
中是否存在连续三项构成等比数列?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0914c295f572c98dd043d4f84268934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9599b8c0f6a10d15f408ad651b35c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6425080aabe41f002230dd5f59ca32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e586e28b5e2d892e5280a912653bb12.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72878dfe2c7a76d76287194ac4bdf4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729b4033af5b0c9c4889406d2c8294f7.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a386e4d3f92631ed64ca3e2f5f4725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
6 . 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:北京卷专题18数列(解答题)
7 . 若有穷整数数列
满足
(
),且各项均不相同,则称
为
数列.对
数列
,设
,
,则称数列
为数列
的导出数列.
(1)分别写出
数列
与
的导出数列;
(2)是否存在
数列
使得其导出数列
的各项之和为0?若存在,求出所有符合要求的
数列;若不存在,说明理由;
(3)设
数列
与
的导出数列分别为
与
,求证:
的充分必要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1692162bb6b1d066d19facf1db9f0124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf551abe94e82f25655f579fe2ce5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a313ae0e4926d7758180c37bc09e0c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75077d8ca056bed47d638a019aa6c798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)分别写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8032e8b31fe607048b2bff947a3a2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155e15b700fb85afe7783a6a017bd2fa.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63be95225b55df87368caaf221adf29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abef087aebad813217c01f8251271d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63be95225b55df87368caaf221adf29e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a115fd7f48a87694f2d8ee533ec7480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75077d8ca056bed47d638a019aa6c798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff10b5d40f7d0e7b92d6bb1902f050b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11e87a6bc5350c44fe1e70aeea7f3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac7a09d1ad5e66b7a532e1cf5b596c0.png)
您最近一年使用:0次
2023-07-09更新
|
311次组卷
|
3卷引用: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)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)北京市朝阳区2022-2023学年高二下学期期末质量检测数学试题【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
名校
8 . 已知有限数列
为单调递增数列.若存在等差数列
,对于A中任意一项
,都有
,则称数列A是长为m的
数列.
(1)判断下列数列是否为
数列(直接写出结果):
①数列1,4,5,8;②数列2,4,8,16.
(2)若
,证明:数列a,b,c为
数列;
(3)设M是集合
的子集,且至少有28个元素,证明:M中的元素可以构成一个长为4的
数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78af5020619465dd4f48090d1c27825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588d22323fe2e6666bb7052a5d686b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3acb298edf3a1af4b0c18396e7c453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(1)判断下列数列是否为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
①数列1,4,5,8;②数列2,4,8,16.
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf36a8b0b9303e515cab436d325cd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(3)设M是集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b598d2cc3e2ea8e6a76670b1feecbad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
您最近一年使用:0次
2021-04-22更新
|
1041次组卷
|
6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)北京市通州区2021届高三年级一模数学试题(已下线)4.2.2 等差数列的通项公式(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)北京首师附中2021~2022学年高二上学期1月月考数学试题北京市师大附中2022-2023学年高二上学期数学期末试题北京市第九中学2024届高三上学期12月月考数学试题
真题
名校
9 . 已知数列
满足:
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8094aae498aec981ce621a032007ce26.png)
.记
集合
.
(Ⅰ)若
,写出集合
的所有元素;
(Ⅱ)若集合
存在一个元素是3的倍数,证明:
的所有元素都是3的倍数;
(Ⅲ)求集合
的元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87397e6df8ed820638eea31e403a94b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69552a67ba83e9c4a70901a5d49a8519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8094aae498aec981ce621a032007ce26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a765bfd025a46459618f5ef76321696a.png)
集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21550abb7c545b53cd2336a7a76885fb.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecf69901899bba130968c7a091790d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅱ)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅲ)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2016-12-03更新
|
3143次组卷
|
13卷引用:重组卷05
(已下线)重组卷05北京十年真题专题06数列专题14数列2015年全国普通高等学校招生统一考试理科数学(北京卷)北京五十七中2017-2018学年高二上学期期中考试数学试题北京市育才学校2022届高三12月月考数学试题北京市第三十五中学2021-2022学年高二6月月考数学试题北京市昌平区第二中学2023届高三上学期期中考试数学试题北京市第十二中学2023届高三上学期12月月考数学试题北京市八一学校2022-2023学年高二下学期3月月考数学试题北京市石景山区京源学校2022届高三高考数学适应性试题北京市育英学校2022-2023学年高二下学期期末练习数学试题(已下线)专题21 数列解答题(理科)-4
10 . 已知
为正整数,数列
:
,记
.对于数列
,总有
,
,则称数列
为
项0-1数列.若数列A:
,
:
,均为
项0-1数列,定义数列
:
,其中
,
.
(1)已知数列A:1,0,1,
:0,1,1,直接写出
和
的值;
(2)若数列A,
均为
项0-1数列,证明:
;
(3)对于任意给定的正整数
,是否存在
项0-1数列A,
,
,使得
,并说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83590c4a7ea5636843dd4b60c67cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6eebdcb5458e76931806d7d001e7d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a492010ae000022884ff8648ab95215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c365eeee68c896623c8a9f4d1a4e0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d64beb75ea4cfc016995a81de4160e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5231cb0bfedf2f963c1830adfd74aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a37472927e5adf5d10ea71516ffdcd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30a09719b90ab0a9344522451d754b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c365eeee68c896623c8a9f4d1a4e0f7.png)
(1)已知数列A:1,0,1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2952a31b68a2bb188ad215e109e7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc53bf6c5c8ac960186362af2158994f.png)
(2)若数列A,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6025c89963745b2f6bb2c45b4e03b225.png)
(3)对于任意给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d3076f01e163e656818cd4999f00ce.png)
您最近一年使用:0次
2022-07-08更新
|
632次组卷
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7卷引用: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)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)北京市海淀区2021-2022学年高二下学期学业水平调研数学试题北京市广渠门中学2022-2023学年高二下学期第一次月考数学试题北京市顺义牛栏山第一中学2022-2023学年高二下学期期末数学复习试题(一)北京市昌平区第一中学2024届高三上学期期中考试数学试题【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)