名校
1 . 设正整数数列
,
,
,
满足
,其中
.如果存在
,3,
,
,使得数列
中任意
项的算术平均值均为整数,则称
为“
阶平衡数列”
(1)判断数列2,4,6,8,10和数列1,5,9,13,17是否为“4阶平衡数列”?
(2)若
为偶数,证明:数列
,2,3,
,
不是“
阶平衡数列”,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246f051291c76972cc3bd4a4f82f2342.png)
(3)如果
,且对于任意
,数列
均为“
阶平衡数列”,求数列
中所有元素之和的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140b9dbcada4ac2e5fe3cc30009bcd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a682c1e08d96bf4dc8d674b4b6a1c920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb62c59018da6ef27b45a210c675129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad48b0279100c0f6958fdba11d84b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3550c48a81ab687bbcdd8fdc6931701f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断数列2,4,6,8,10和数列1,5,9,13,17是否为“4阶平衡数列”?
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f344a2d8d76fad8cbecaffc44f11f907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246f051291c76972cc3bd4a4f82f2342.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0da1b6e7328f7540c2e964874fbc4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246f051291c76972cc3bd4a4f82f2342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2024-01-14更新
|
1113次组卷
|
9卷引用:上海市吴淞中学2021-2022学年高二上学期期末数学试题
上海市吴淞中学2021-2022学年高二上学期期末数学试题(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)云南省昆明市云南师范大学实验中学2023-2024学年高二下学期3月月考数学试题北京西城区2019届高三上学期期末数学(理)试题(已下线)数学-2022届高三下学期开学摸底考试卷(北京专用)(已下线)北京市第四中学2022届高三下学期开学考试数学试题北京市第三中学2023届高三上学期期中学业测试数学试题北京市陈经纶中学2023届高三下学期综合练习一(开学考试)数学试题2024年普通高等学校招生全国统一考试数学冲刺卷一(九省联考题型)
名校
解题方法
2 . 若各项为正的无穷数列
满足:对于
,
,其中
为非零常数,则称数列
为
数列.记
.
(1)判断无穷数列
和
是否是
数列,并说明理由;
(2)若
是
数列,证明:数列
中存在小于1的项;
(3)若
是
数列,证明:存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782fdf6345302a3d8814acf96f6b3acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
(1)判断无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93068e5f0dedec981ec828ffa4458c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446e8a7985d4d3dd95c70dc4aad67861.png)
您最近一年使用:0次
2024-01-04更新
|
1522次组卷
|
3卷引用:广西南宁市第二中学2023-2024学年高二下学期开学考试数学试卷
名校
3 . 已知数列A:a1,a2,…,aN
的各项均为正整数,设集合
,记T的元素个数为
.
(1)①若数列A:1,2,4,5,求集合T,并写出
的值;
②若数列A:1,3,x,y,且
,
,求数列A和集合T;
(2)若A是递增数列,求证:“
”的充要条件是“A为等差数列”;
(3)请你判断
是否存在最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485eb1ad5fd643e739e15a39c7922b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f081d422da2385bed320a2c3a52633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f812114476c7a8f0219a412039d07c89.png)
(1)①若数列A:1,2,4,5,求集合T,并写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f812114476c7a8f0219a412039d07c89.png)
②若数列A:1,3,x,y,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c73a0da1caaab9022852df736dc9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c4c7fe993913d8731716ac796359f0.png)
(2)若A是递增数列,求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5dd1d57123aedb635394b03c8b4c461.png)
(3)请你判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f812114476c7a8f0219a412039d07c89.png)
您最近一年使用:0次
2023-12-30更新
|
723次组卷
|
7卷引用:北京市北京大学附属中学2021-2022学年高二上学期期中数学试题
北京市北京大学附属中学2021-2022学年高二上学期期中数学试题北京市第二十四中学2023-2024学年高二上学期期末数学模拟试卷(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21(已下线)专题03 条件存在型【讲】【北京版】1广东省惠州市第一中学2024届高三元月阶段测试数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)高考数学冲刺押题卷01(2024新题型)
4 . 设数列
的前
项和为
.若对任意的正整数
,总存在正整数
,使得
,则称
是“
数列”.
(1)若数列
,
,判断
和
是否是“
数列”;
(2)设
是等差数列,其首项
,公差
.若
是“
数列”,求
的值;
(3)证明:对任意的等差数列
,总存在两个“
数列”
和
,使得
成立.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3693c7c942afef5517a3c18997c878df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e903c3dc6bdb559fd173f8d4e930f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ff259bff098430a6512d0e4f6fb2d9.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/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)设
![](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/d2d8bbb4a09e0ac86bbae46222a90841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(3)证明:对任意的等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.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/50a13fcd18316e035cdc08901073672e.png)
您最近一年使用:0次
2023-12-25更新
|
766次组卷
|
4卷引用:上海市松江二中2023-2024学年高二上学期期末考试数学试题
名校
5 . 设
为给定的正奇数,定义无穷数列
:
若
是数列
中的项,则记作
.
(1)若数列
的前6项各不相同,写出
的最小值及此时数列的前6项;
(2)求证:集合
是空集;
(3)记集合
正奇数
,求集合
.(若
为任意的正奇数,求所有数列
的相同元素构成的集合
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77576292d833c93bdcf4da9787ee0db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003dd0feaa12a01db4c777784889c374.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3884cadaff5a78756698d57c41f305d.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611448a63d973f73f8c0026dd38ac932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7dbf7c1220f9db7d313570143f4a709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-12-21更新
|
1111次组卷
|
5卷引用:4.3 数列-求数列通项的八种方法(八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)4.3 数列-求数列通项的八种方法(八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)北京市西城区北师大附属实验中学2024届高三上学期12月月考数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)练湖南省2024届高三数学新改革提高训练二(九省联考题型)(已下线)拔高点突破01 集合背景下的新定义压轴解答题(四大题型)
名校
解题方法
6 . 若数列
满足:
,且
,则称
为一个
数列.对于一个
数列
,若数列
满足:
,且
,则称
为
的伴随数列.
(1)若
数列
中,
,写出其伴随数列
中
的值;
(2)若
为一个
数列,
为
的伴随数列
①证明:“
为常数列”是“
为等比数列的充要条件;
②求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0b585b9c5b459de9186779aba4030d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.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/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b0b282d53c9467e0ec983fed79c622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f36f5e8a5983a1413e3f63f35c7cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8ae4555eacf411d0a8867d9970668.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325629d6ef791f80f37af613adcf92fd.png)
您最近一年使用:0次
2023-12-11更新
|
1303次组卷
|
2卷引用:北京市第五十五中学2023-2024学年高二上学期12月月考数学试卷
名校
解题方法
7 . 已知数列
:
,
,…,
.如果数列
:
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba977bedd76ef240d07fde83894bbe8.png)
满足
,
,其中
,则称
为
的“衍生数列”.
(1)若数列
:
,
,
,
的“衍生数列”是
:5,
,7,2,求
;
(2)若
为偶数,且
的“衍生数列”是
,证明:
的“衍生数列”是
;
(3)若
为奇数,且
的“衍生数列”是
,
的“衍生数列”是
,…依次将数列
,
,
,…第
(
)项取出,构成数列
:
,
,
….求证:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.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/8ba977bedd76ef240d07fde83894bbe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7e6327ecd86c682863f4a89e619fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da65bfc5919df189631c53048808e4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0171d0cea7070a6536e0c756b6907e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.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/a821e643d5fae24caed0faa6d423dad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab46d077ba3d6e13fa1f6a5aaa0ce6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452b9bcf720355d0678d62cbf6857ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f4ddebf0e34a5c3e9232ae66709aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452b9bcf720355d0678d62cbf6857ffe.png)
您最近一年使用:0次
2023-11-23更新
|
453次组卷
|
4卷引用:宁夏回族自治区2023-2024学年高二上学期期末测试数学训练卷(二)(范围:选择性必修第一册 第三章+选择性必修第二册 第四章)
宁夏回族自治区2023-2024学年高二上学期期末测试数学训练卷(二)(范围:选择性必修第一册 第三章+选择性必修第二册 第四章)北京市汇文中学2023-2024学年高三上学期期中考试数学试题(已下线)压轴题数列新定义题(九省联考第19题模式)练(已下线)黄金卷06
名校
解题方法
8 . 已知数列
,若对于任意正整数n,
仍为数列
中的项,则称数列
为“回归数列”.
(1)已知
,判断数列
是否为“回归数列”,并说明理由;
(2)若数列
为“回归数列”,且对于任意正整数n,均有
成立,证明:数列
为等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0f19bd1a86a8afc3ee490101ca6988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3234c284ab8de4d566290e20fdc50900.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/df3054785bacfe0537831c337f57ab92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
9 . 在数字
的任意一个排列
:
中,如果对于
,
,有
,那么就称
为一个逆序对.记排列
中逆序对的个数为
.如
时,在排列
:3,2,4,1中,逆序对有
,
,
,
,则
.
(1)设排列
:
,写出两组具体的排列
,分别满足:①
,②
;
(2)对于数字1,2,…,n的一切排列
,求所有
的算术平均值;
(3)如果把排列A:
中两个数字
交换位置,而其余数字的位置保持不变,那么就得到一个新的排列,
:
,求证:
为奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5929d3faf0bb567573cc46fabd30aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6d99dfbc36d9be71895dfdb732f321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f2c7c9305b404f7363a376af101aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ae1214cc78e72fb613d7e649bc27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a1d999ab14d86a73dd17df33f23b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bba7a40102e81f5759f7b05ebf5a18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0481d24e2af1e0cd348732b9444d1dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce2830528c2ea6b5d4df0c77644e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b08a341f6e37e92710bf95531217e6.png)
(1)设排列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42030a33382b003b81c2b148a216fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb79a2396402d62e725578f015e5c06a.png)
(2)对于数字1,2,…,n的一切排列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bba7a40102e81f5759f7b05ebf5a18c.png)
(3)如果把排列A:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e68f643eb061dea7def83952c1f56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3d172f08313520e76b6cbc2ff9980c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c687695f558d18f8b220be874a723170.png)
您最近一年使用:0次
10 . 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)
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