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
|
1095次组卷
|
9卷引用:北京西城区2019届高三上学期期末数学(理)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)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
2 . 记
表示集合A中的元素个数,
.若
,则称集合A有“性质T”.
(1)设
为等比数列且各项为正有理数,证明集合A有“性质T”.
(2)已知集合A,B均有“性质T”,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4978089eb165d2241a35275396794d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181891d7f4b616b13ced728f4e2528b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b996fe0e5156e59dd71b5e64ded28829.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922f1456841b9203279ed22138c46428.png)
(2)已知集合A,B均有“性质T”,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080b2789c3db78a2e6419eca85543091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e46f31e6dd0ef18885c3756005b371.png)
您最近一年使用:0次
名校
解题方法
3 . 对于数列
,若存在常数
,对任意的
,恒有
,则称数列
为
数列.
(1)首项为1,公比为
的等比数列
是否为
数列?请说明理由;
(2)设
是数列
的前
项和,若数列
是
数列,那么数列
是否为
数列?若是,请说明理由;若不是,请举出一个例子;
(3)若数列
,
都是
数列,求证:数列
是
数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d4f5886b62640f2638d7e9580a51d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866d003eaa6187770f751425fac96dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d4f5886b62640f2638d7e9580a51d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
(1)首项为1,公比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc0bdefe6ea4cc508dd42ee6061106b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67dad7337d3daaaae14dfb7ea8591fa.png)
您最近一年使用:0次
2023-01-31更新
|
420次组卷
|
2卷引用:北京一零一中学2021届高三上学期10月统考(二)数学试题
20-21高三上·上海浦东新·阶段练习
名校
解题方法
4 . 设
是正整数,一个有限整数数列
,定义它的差集A为
构成的集合.
(1)求下列数列的差集A;
①1,2,3,4,5,6,7,8;
②1,2,4,8,16,32
(2)若
,
,求
的最大值和最小值;
(3)若
,并且
,求满足上述要求的整数列的个数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212c82587ab19801f2646fd69abc79e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0169119ec74ae04e129ed0046ae97dc6.png)
(1)求下列数列的差集A;
①1,2,3,4,5,6,7,8;
②1,2,4,8,16,32
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c7867969b14fd642147188b6ebf29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374445bb53a8d1c11c2e47f2a0c9e0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc684a3a6aef07bfb1dff85792c2a1c3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795c5b51ed46ce5ff453748652f0121c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f83fb5a9c7eeccc302a8a84ada9340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae48677f8f6e1eaa980756a18378e593.png)
您最近一年使用:0次
真题
解题方法
5 . A是由定义在
上且满足如下条件的函数
组成的集合:①对任意的
,都有
;②存在常数
,使得对任意的
,都有
.
(1)设
,证明:
;
(2)设
,如果存在
,使得
,那么这样的
是唯一的;
(3)设
,任取
,令
,证明:给定正整数k,对任意的正整数p,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de71d25c72850e383a4c841eed0db99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2775ffdf695af2d263f0ea93ac5904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4031c9cbbcbbecfc0a8ca5490647e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5d880d349c00a3f81f830bb35e1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d03b29af4e3206af656a142d17657f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799650ddf5fb8e7c91cf59163aa1b7a4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1dbdb8423d86a92629b081ae2b2154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5528f643fe7e0449e48c8f81b16b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e599070e5874ed4a9478f5260b98e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0d7024ce3371628f09963f9a976ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dcca902b1982e13aeea5d094bb6016.png)
您最近一年使用:0次
6 . 已知数列
满足
,
,并且
,
(
为非零参数,
).
(1)若
成等比数列,求参数
的值;
(2)当
时,证明:
;
(3)当
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad5eee51276c36c3b0ec5473504958a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6c7c4c02de4c67f60d31ed1139bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3706c8575b004154908c34c973feba03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4159df4d2540cc3909c26128314e82e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c77422a29ac2408a030888c50042c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ec0b97655e6bd7004df04457c493ac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc321d11e01d8b1ef4879278eb385f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323c36bb62b2165b80aa4d388901a086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8047f0a8bd0cf4e250cd0fe80093b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/396c3d8c0d5b9d36dcfcde77865960d8.png)
您最近一年使用:0次
7 . 设
,如图,已知直线
及曲线
,C上的点
的横坐标为
.从C上的点
作直线平行于x轴,交直线l于点
,再从点
作直线平行于y轴,交曲线C于点
.
的横坐标构成数列
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/92c5f778-0f93-434c-907c-a08340ef4426.png?resizew=190)
(1)试求
与
的关系,并求
的通项公式;
(2)当
时,证明
;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2df29bc4b98cfcc6a3237b5fef779e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c190e3498ab082d575c24a1a66b6da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324872ecd041f6174655abf830019615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a753812145824f98f997029f5a7439e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908164d96d0438801a4f4aefebdf3aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e240e2923edaf859466663a10ebe77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/92c5f778-0f93-434c-907c-a08340ef4426.png?resizew=190)
(1)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57755d3087d086f83e1b6f37723d2869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4ee8097d2c1659752dda9d86603f70.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa634182cc0ec75b9fd5d0db429d74b9.png)
您最近一年使用:0次
8 . 称一个复数数列
为“有趣的”,若
,且对任意正整数n,均有
.求最大的常数C,使得对一切有趣的数列
及任意正整数m,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b670aca396b96eaf2c553b1ca84486dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a383b03b4869ea984d58b8d87c35402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7763a0445ba78bceb1bc24a9f1010f5c.png)
您最近一年使用:0次
2022-10-15更新
|
354次组卷
|
4卷引用:2019年全国高中数学联赛A卷
名校
解题方法
9 . 如果一个数列从第
项起,每一项与它得前一项得差都大于
,则称这个数列为“
”数列.
(1)若数列
为“
数列”,且
,
,
,求实数
的取值范围;
(2)是否存在首项为
的等差数列
为“
数列”,且其前
项和
满足
?若存在,请求出
的通项公式;若不存在,请说明理由;
(3)已知等比数列
的每一项均为正整数,且
为“
数列”,
,
,当数列
不是“
数列”时,试判断数列
是否为“
数列”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129d17c9a49272d44a0e70346414d12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129d17c9a49272d44a0e70346414d12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f73a97d20f5bc6ce114cd7ae7845c009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b1bfb98c2ca5473a25db8e422aa3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f89df42fedf7bee8a1756c7e4b7488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)是否存在首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9862c3f79df375b515dc9f707c763444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.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/a041c7a8d92b961e1d401ec7729b0e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(3)已知等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16a90364bdffdb10175942d399cc895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c22fc9b4692629ca685f0db29c9837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf12761b39f2d4f01cc505569dc4c58.png)
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名校
解题方法
10 . 若定义在
上的函数
满足:对于任意实数
,总有
恒成立,我们称
为“类余弦型”函数.
(1)已知
为“类余弦型”,且
,求
和
的值;
(2)在(1)的条件下,定义数列
(
),求
的值;
(3)若
为“类余弦型”,且对任意非零实数
,总有
,证明:
①函数
为偶函数;
②设有理数
满足
,判断
和
的大小关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146ff57d46a7f258604e9660a726fdba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5459c2261022c328d84056a6a8e4e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365f5ac9c0d75ff80bd10f9924cfdd80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c228ab4a1edb2af494ff1d7c898518.png)
(2)在(1)的条件下,定义数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa8f9855ba25451049aa4630023e6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4a303c19edd204b3909c79c9a7632a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2316f10f32fb86134073f413f7a7b14.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d75465362a8dc41f4c3155ecb63f17.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②设有理数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a0b534b683b7e7210a261211af142a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915b3d29d0c7dd83c188e3ce31f52fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a4bf4bb3622d9396a2d975e96558a2.png)
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