名校
1 . 对于数列
,如果存在一个正整数
,使得对任意的
都有
成立,那么就把这样一类数列
称作周期为
的周期数列,
的最小值称作数列
的最小正周期,以下简称周期.例如当
时
是周期为1的周期数列,当
时
是周期为4的周期数列.
(1)设数列
满足
不同时为0
,求证:数列
是周期为6的周期数列,并求数列
的前2013项的和
;
(2)设数列
的前
项和为
,且
.
①若
,试判断数列
是否为周期数列,并说明理由;
②若
,试判断数列
是否为周期数列,并说明理由;
(3)设数列
满足
,数列
的前
项和为
,试问是否存在
,使对任意的
都有
成立,若存在,求出
的取值范围;不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef65559a6b44930addc23adeb8d854c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126141b8d68abc6a0823fade2f1b8127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082e8fd18cc10f578020188f254a2455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c002bdb39554b14fb5493781924069a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15987d51b64254b36a00be900799d166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.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/e4a67afce3eba3ca099670e3ded418d9.png)
(2)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/5c07ba166ca9af1ffde9dd49876b17a4.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38ac38efc5f58e833f21c725e9711c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29a7d539f5f39eecf615febf9862109.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/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042896d1702c2c0345f21b63d35d766a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
您最近一年使用:0次
2 . 已知数集
具有性质P:对任意的i,j(
),
与
两数中至少有一个属于M.
(1)分别判断数集
与
是否具有性质P,并说明理由;
(2)证明:
,且
;
(3)当
时,证明:
,
,
,
,
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5579e321a3de8e782038ae8d6e8086e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae331839bce8f3c14d7efd7f9d8915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1906b96e054c5e74d295b61149a36b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ca464b4151405a89cf83e6fb41e580.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a4bf8d30875aced4b311818ef754e8.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
您最近一年使用:0次
3 . 已知数表
中的项
互不相同,且满足下列条件:①
;②
.则称这样的数表
具有性质
.
(1)若数表
具有性质
,且
,写出所有满足条件的数表
,并求出
的值;
(2)对于具有性质
的数表
,当
取最大值时,求证:存在正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647e52202e18fa269763df9933db6973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e3cb3f545929654a1197de7698b153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e002706ff896b1172db9a84e132ca787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bd58d80ed7062213c8f5f3b87bc17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce9d40adaecd9741d39abc0b3690431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eba1bc1bfc3def75c03f2c473330af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce9d40adaecd9741d39abc0b3690431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891f611bbc4558380467c4b4016092a9.png)
(2)对于具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1f8d904832b90d93d8bf482bf210fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887e3ada737ca3af0aa44846dec91a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d42cc575e90606d0fda516f1023c213.png)
您最近一年使用:0次
2023-06-14更新
|
122次组卷
|
2卷引用:北京市第十九中学2022-2023学年高二下学期期中考试数学试题
名校
4 . 若项数为
的数列
满足:
,且存在
,使得
,则称数列
具有性质P.
(1)①若
,写出所有具有性质P的数列
;
②若
,写出一个具有性质P的数列
;
(2)若
,数列
具有性质P,求
的最大项的最小值;
(3)已知数列
均具有性质P,且对任意
,当
时,都有
.记集合
,
,求
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adcce353c3ced76645069760bdf8fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad107fc0e55e4b35b2b25b10f75f4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96b51d9b57fb8f9577f575261c08206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0265ce589cdf60588c9f86671a256992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc147c3c0863d22533a820cc469bfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818b44478f6d1d972aa5bf6dd4d3a0c.png)
(1)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a215612787e43d28bfebc840c3903b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1ddc5b7f288c044f394fd7055e2564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7aa41f0d2bd18825f741a3cc2adef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645ae0b78ad4ca300e3889ca3f9bcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645ae0b78ad4ca300e3889ca3f9bcce.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719c07413b9a867b83f27f5eed752846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6119a01b55a29adabf43ddb2a5211e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0504794eebd6814a3138e796666bca01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191929f42f9053e7355a1a9068ba072f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5975dbb4789b4b2d8f2f0eb3abb4da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc47ee887b63cdc46fdb17dcb75f2f4.png)
您最近一年使用:0次
2023-06-01更新
|
716次组卷
|
3卷引用:北京市西城区北京师范大学附属实验中学2022-2023学年高二下学期期中考试数学试卷
名校
5 . 已知
为有穷数列.若对任意的
,都有
(规定
),则称
具有性质
.设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c38cc7f201fede1860f9fe987ff01e.png)
(1)判断数列
,
是否具有性质
?若具有性质
,写出对应的集合
;
(2)若
具有性质
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519e46609069838b08721bdd8fd7fa6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a427d86ca98786e25d636f58129831cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7e9edf6d0468e0f8ca78b8bac63bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b740bc48c9718a294c11a1485fd14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c38cc7f201fede1860f9fe987ff01e.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4811d7682bd33251b78071ba9ccc66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6bdcbd453ca29c88f9920aa0d15ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed1adc648cc7d8fe7ac43df4b918f11.png)
您最近一年使用:0次
2023-05-20更新
|
198次组卷
|
2卷引用:北京市昌平区前锋学校2022-2023学年高二下学期期中考试数学试题
6 . 已知数列
是以
为首项的常数列,
为数列
的前n项和.
(1)求
;
(2)设正整数
,其中
.例如:
,则
,
;
,则
,
.若
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bdbde4eb7e4d4033bb9053b6c806e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78ef9e9e15ee6c85d553e693ab0a8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e969c6e0cbf06966c3278e392ea5024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d658b93ab4c3343118d949195929f1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2555a7889a95a7c4f8817340843c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87b3590ca6609bd42762651f2a5d952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67cdc410f45ec42010c2932cd2193e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9177079f486c050f336ac20c3c9296d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648e47bfa65ed317328a327b24d109c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-05-20更新
|
316次组卷
|
4卷引用:山东省德州市2022-2023学年高二下学期期中数学试题
山东省德州市2022-2023学年高二下学期期中数学试题(已下线)模块三专题2 数列的综合问题 【高二下人教B版】(已下线)模块三 专题4 数列的综合问题 【高二下北师大版】吉林省白山市抚松县第一中学2022-2023学年高三第十一次校内模拟数学试题
名校
7 . 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)
您最近一年使用:0次
2023-05-19更新
|
200次组卷
|
2卷引用:北京市北京师范大学第二附属中学2022-2023学年高二下学期期中考试数学试题
8 . 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
9 . 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
10 . 若对于正整数k,
表示k的最大奇数因数,例如
,
设
.
(1)求
的值;
(2)求
,
,
的值;
(3)求数列{
}的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91eb1a74ed4eb789a5cf6bf0d08900a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5053a9fb67fdaa4aa847859eaab3a4d.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec264fc10e5d2da798405b6e2f2b577.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c2dfac99c87f0ed79b91f70a26c9d4.png)
(2)求
![](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)
(3)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-05-11更新
|
175次组卷
|
5卷引用:北京市海淀区北京理工大学附属中学2022-2023学年高二下学期期中练习数学试题
北京市海淀区北京理工大学附属中学2022-2023学年高二下学期期中练习数学试题(已下线)模块三专题2 数列的综合问题 【高二下人教B版】(已下线)模块三 专题4 数列的综合问题 【高二下北师大版】北京高二专题02数列(第一部分)(已下线)模块三 专题3 高考新题型专练(专题2:新定义专练)(北师大)(高二)