1 . 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:北京市海淀区2021届高三下学期期中数学试题
解题方法
2 . 郑州中原福塔的外立面呈双曲抛物面状,造型优美,空中俯瞰犹如盛开的梅花绽放在中原大地,是现代建筑与艺术的完美结合.双曲抛物面又称马鞍面,其在笛卡尔坐标系中的方程与在平面直角坐标系中的双曲线方程类似.双曲线在物理学中具有很多应用,比如波的干涉图样为双曲线、反射式天文望远镜利用了其光学性质等等.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/bf236b19-4976-41fd-8f2a-75fac65c6787.png?resizew=142)
(1)已知
,
是在直线
两侧且到直线
距离不相等的两点,
为直线
上一点.试探究当点
的位置满足什么条件时,
取最大值;
(2)若光线在平滑曲线上发生反射时,入射光线与反射光线关于曲线在入射点处的切线在该点处的垂线对称.证明:由双曲线一个焦点射出的光线,在双曲线上发生反射后,反射光线的反向延长线交于双曲线的另一个焦点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/bf236b19-4976-41fd-8f2a-75fac65c6787.png?resizew=142)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84dad5bc5d125b971555d6d4390f662c.png)
(2)若光线在平滑曲线上发生反射时,入射光线与反射光线关于曲线在入射点处的切线在该点处的垂线对称.证明:由双曲线一个焦点射出的光线,在双曲线上发生反射后,反射光线的反向延长线交于双曲线的另一个焦点.
您最近一年使用:0次
2021-04-30更新
|
1393次组卷
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5卷引用:江苏省六校2021届高三下学期第四次适应性联考数学试题
江苏省六校2021届高三下学期第四次适应性联考数学试题(已下线)专题3.8 双曲线的综合问题-2021年高考数学解答题挑战满分专项训练(新高考地区专用)(已下线)江苏省南通市如皋市2022-2023学年高三上学期9月诊断测试数学试题(已下线)专题25 圆锥曲线的光学性质及其应用 微点2 双曲线的光学性质及其应用(已下线)专题3.9 直线与双曲线的位置关系-重难点题型精讲-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)
名校
解题方法
3 . (1)已知集合
,求实数
的取值范围;
(2)在
上定义运算“
”:
,若存在
,使不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe1aac30bebf3d96648a9171b52ad71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7d51315fcca519cb58bacd0040d7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02048c3b1e13de7991e4a8db3e71973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69acebdcbf2c7716a0f42d04fef3a5c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-08-23更新
|
383次组卷
|
7卷引用:江苏省南京市第十二中学2020-2021学年高一上学期10月学情调研数学试题
名校
解题方法
4 . 集合
是由满足以下性质的函数
组成:①
在
上是增函数;②对于任意的
,
.已知函数
,
.
(1)试判断
,
是否属于集合
,并说明理由;
(2)将(1)中你认为属于集合
的函数记为
.
①试用列举法表示集合
;
②若函数
在
(
)上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612196a90762a81ea26e4edf26e8d648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065206af6d87dc50ae77490101d84842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ef8e2eecaec66e2d89ab591a14c3b.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548636534994cd465dfc7bf7dd41505b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)将(1)中你认为属于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①试用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb056bf37936d6687071d6003cb1559.png)
②若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be466586da8810ccfd811c59a747adb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239a6b1f713ef38f2b613697d5daaf51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
5 . 已知数列A:
的各项均为正整数,设集合
,记T的元素个数为
.
(1)若数列A:1,2,4,3,求集合T,并写出
的值;
(2)若A是递增数列,求证:“
”的充要条件是“A为等差数列”;
(3)若
,数列A由
这
个数组成,且这
个数在数列A中每个至少出现一次,求
的取值个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341148b74364c392ae38dd5a26cd9d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f491a8e9ecacc5cbd90155154d9adf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(1)若数列A:1,2,4,3,求集合T,并写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(2)若A是递增数列,求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3197c615558fee3993d2a8deb9091f0a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c708779abd03bff972ca72ed5a9453e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a1963f19675193bd3f24c5404b69db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
您最近一年使用:0次
2021-04-07更新
|
1511次组卷
|
9卷引用:北京市西城区2021届高三一模数学试题
6 . 某种“笼具”由内、外两层组成,无下底面,内层和外层分别是一个圆锥和一个圆柱,其中圆柱与圆锥的底面周长相等,圆柱有上底面,制作时需要将圆锥的顶端剪去,剪去部分和接头忽略不计,已知圆柱的底面周长为
,高为
,圆锥的母线长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/f993817e-a528-4a51-bf47-6f5c006d2614.png?resizew=103)
(1)求这种“笼具”的体积(
,结果精确到
);
(2)现要使用一种纱网材料制作50个“笼具”,该材料的造价为每平方米8元,共需多少元?(
,结果精确到1元)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea42be3fdbd222da17bf0fe91046fa49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668a3f3ce5b8a272ad92c2ebd233f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/f993817e-a528-4a51-bf47-6f5c006d2614.png?resizew=103)
(1)求这种“笼具”的体积(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d553e4a26eb3012410ef7558a5fd6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ea4449895040ce4813b038324ef1a5.png)
(2)现要使用一种纱网材料制作50个“笼具”,该材料的造价为每平方米8元,共需多少元?(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d553e4a26eb3012410ef7558a5fd6d.png)
您最近一年使用:0次
2022-08-19更新
|
710次组卷
|
18卷引用:安徽省合肥市第一中学2017-2018学年高二上学期段一考试(月考)数学(文)试题
安徽省合肥市第一中学2017-2018学年高二上学期段一考试(月考)数学(文)试题安徽省合肥市第一中学2017-2018学年高二上学期月考文数试题(已下线)2019年1月2日 《每日一题》人教必修1+必修2(上学期期末复习)空间几何体的表面积与体积山西省朔州市怀仁市2019-2020学年高二上学期第四次月考数学试题上海市金山中学2015-2016学年高二下学期期中数学试题上海市普陀区2016届高三上学期12月调研(文科)数学试题2020届上海市高三高考模拟2数学试题安徽省滁州市定远县育才学校2020-2021学年高二上学期第一次月考数学(文)试题上海市位育中学2020-2021学年高二下学期期中数学试题(已下线)【师说智慧课堂】高一数学数学新教材必修二练习题(已下线)专题13 空间几何体-备战2022年高考数学学霸纠错(全国通用)黑龙江省大庆市大庆中学2021-2022学年高一下学期期中考试数学试题(已下线)专题21 空间几何体(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)苏教版(2019) 必修第二册 过关斩将 第13章 13.3.2 空间图形的体积(已下线)第01讲 基本立体图形、简单几何体的表面积与体积 (高频考点—精练)上海市徐汇中学2022-2023学年高二上学期期中数学试题上海市松江二中2022-2023学年高二上学期期中数学试题(已下线)期中测试卷02(测试范围:第10-11章+空间向量与立体几何)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
名校
7 . 在平面上,给定非零向量
,对任意向量
,定义
.
(1)若
=(-1,3),
=(2,3),求
;
(2)若
=(2,1),位置向量
的终点在直线x+y+1=0上,求位置向量
终点轨迹方程;
(3)对任意两个向量
,求证∶
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9181079d14f7c1bc9b5b2624f94edca.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(3)对任意两个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1721476f7850842ba3dc3d8be33c3723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835ebae7895448fd3d6551b953565ab3.png)
您最近一年使用:0次
解题方法
8 . 阅读材料:我国著名数学家华罗庚先生曾说:“数缺形时少直观,形少数时难入微,数形结合百般好,隔离分家万事休.”在数学的学习和研究中,常用函数的图象来研究函数的性质,也常用函数的解析式来琢磨函数的图象特征.我们来看一个应用函数解析式研究对应函数图象形状的例子.对于函数
,我们可以通过解析式来研究它的图象和性质,如:图象特征:
(1)在函数
中,由
,可以推测出,对应的图象不经过
轴,即图象与
轴不相交;由
,可以推测出,对应的图象不经过
轴,即图象与
轴不相交;
(2)在函数
中,当
时
,当
时
,可以推测出,对应的图象能分布在第一、三象限;
(3)在函数
中,若
,则
,且当
逐渐增大时,
逐渐减小,可推测出,对应的图象越向右越靠近
轴;若
,则
,且当
逐渐减小时,逐渐增大,可以推测出,对应的图象越向左越靠近
轴;
(4)由函数
可知
,即函数
是奇函数,可以推测出,对应的图象关于原点对称.
结合以上性质,逐步猜想出函数
对应的图象,如图所示:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/a92be779-4fce-4c0c-b960-f436d804f6b4.png?resizew=140)
尝试类比,探究函数
的图象,写出图象特征,并根据你得到的结论,尝试作出函数对应的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
(1)在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c412d5329ba909164329663b7eecdfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57458464618fcf619375a93d3c66d69.png)
(3)在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842c2ef9893cc67e621e272fa0be9926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57458464618fcf619375a93d3c66d69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(4)由函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1db6c94b94afc372212a81cc1f4dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
结合以上性质,逐步猜想出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/a92be779-4fce-4c0c-b960-f436d804f6b4.png?resizew=140)
尝试类比,探究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c478693312b42c5dd5f88945f4b746.png)
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名校
解题方法
9 . 设集合
,且S中至少有两个元素,若集合T满足以下三个条件:①
,且T中至少有两个元素;②对于任意
,当
,都有
;③对于任意
,若
,则
;则称集合
为集合
的“耦合集”.
(1)若集合
,求集合
的“耦合集”
;
(2)若集合
存在“耦合集”
,集合
,且
,求证:对于任意
,有
;
(3)设集合
,且
,求集合S的“耦合集”T中元素的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b94a0abdcc3807bf392db9ff45b065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eee24115b5913c454fe5a93f176db80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7741c8d8f0486556a102d904fb26a7be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8339eab9c659e50db86828b65f825e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566d386cbedb1c8750f4837633c2af64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0086b15b30b83d428b35cdbe094810f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5718e9c8baa106b447f9fae23e730de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a8b2c7049b225429ace45c69a44d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a09b275c36edd90e33b7dbd4d8a1ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799794fea82a353250cb5d27a30002cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499f74ed37d11fb9d30d9ee10c337c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b19fb48a58c310c0432c93e054c26ff.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e91972c88f7dcf857a74fdbd57deb0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa09412f1c12451c54596ce4d58fffa.png)
您最近一年使用:0次
2021-01-27更新
|
1320次组卷
|
5卷引用:北京市顺义区2020-2021学年高一上学期期末考试数学试题
10 . 给定正整数m,t(
),若数列A:
满足:
,
,
,则称数列A具有性质
.
对于两个数列B:
;C:
,
定义数列
;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1666128b812bc56253aee5932dada0.png)
(1)设数列A具有性质
,数列
的通项公式为
(
),求数列
的前四项和;
(2)设数列
(
)具有性质
,数列B满足
,
,
,
且
(
).若存在一组数列
,使得
为常数列,求出m所有可能的值;
(3)设数列
(
)具有性质
(常数
),数列B满足
且
(
).若存在一组数列
,使得
为常数列,求k的最小值.(只需写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e731fd8ce3511a486bbe95e7199450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da18ad56af5e38b1a5b73f44ba198fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a406d53fd6ffd9ee6cd914f5e2b0a9bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2e48e217357ba34d190e07a6149e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cb8986f17cfca98e7faa063abc09f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef30011e8c2425db431204436e16629.png)
对于两个数列B:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a974a6a4d453dbb22a7b599e36f451d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae1beb8a070d3672795b2cf64ec1da6.png)
定义数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d805b6e79f2bd12ea9deda3e14261a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1666128b812bc56253aee5932dada0.png)
(1)设数列A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708011e87fae90efc444a7477512aac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00725492cf521a4277f03c364998a4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17c7608edaf9a0fa498674d5c729ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e96fafcc7b7f783d436f853449208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fcabace2d41a5fb549da9d88c3ad33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cf909f2febeea7d169459d0cf0bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fe300fb6c2065f7a3783d24d9c0010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1109ca176d2be47347f68a3de238abd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9d48660f696fc51b97c89fa55d6f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed97ab77f50ae6311b37a0678ead43d5.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00725492cf521a4277f03c364998a4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ee076644544f8a5f9ad2ae537ba7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d438267fddcd02afff8e73c6c3fec8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4502c640ee65eb3f11364fb461c69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef78e554041f64aecdc9ca4e037b58c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1109ca176d2be47347f68a3de238abd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9d48660f696fc51b97c89fa55d6f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed97ab77f50ae6311b37a0678ead43d5.png)
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