名校
解题方法
1 . 已知数列
满足
,且
,
,则该数列的首项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
______ ;若数列
的前
项的为
,且对
都有
恒成立,则实数
的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d5b808093f929e7b386331b14ce7271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42508dd2bbf426186f64c45c9696626d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c89f409e64a565173de4721d5e461c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87c09e6f0e846dd34d4eb139656afac.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/f1278e6fd6266a7dc9c39b10260db642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0d4f4f820dba1879b6fc5a530ee717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2022-05-09更新
|
523次组卷
|
2卷引用:湖南省岳阳市平江县2022届高三下学期教学质量监测(三)数学试题
2 . 对于集合
的子集
,定义
的“特征数列”为
,
,
,
,其中
,其余项均为0,例如子集
的“特征数列”为0,1,1,0,0,
,0.
(1)子集
的“特征数列”的前四项和等于______ ;
(2)若
的子集
的“特征数列”
,
,
,
满足
,
,
,
的子集
的“特征数列”为
,
,
,
,满足
,
,
,则
的元素个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ac7097b94b5186426d0fb8f472d507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e54c671b678b9eb9bd214464da9eecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e4c6544ede4573bd9a07d116f5cfb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506d1ac280b71c631cd4e9b63d009ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bb95534f703ac3e6328ef5be7a9f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
(1)子集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2afe5df0efa1789351558a18a0bef6e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b92cba1ed694b1a11411fa274ff7c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5cfb0d2cf24c1da7ba972e0218a974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc1a195f904c8292c2db380466d139f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed794854ded63e016e678e467b5c6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c02e55edaf83351e20283be2048b0a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d563dc363f21db86f5525ac9bc29e1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a0528184538fe671ad0f579ef51d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243ecc5a0f9ecaacb11b6c1d3c7726ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4afabfd5b4885311f8d9a4bcf791b71.png)
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2022-04-28更新
|
863次组卷
|
3卷引用:湖南省长沙市雅礼中学2022届高三下学期一模数学试题
名校
3 . 德国数学家康托尔是集合论的创始人,以其名字命名的“康托尔尘埃”作法如下:第一次操作,将边长为1的正方形分成9个边长为
的小正方形后,保留靠角的4个,删去其余5个;第二次操作,将第一次剩余的每个小正方形继续9等分,并保留每个小正方形靠角的4个,其余正方形删去;以此方法继续下去……、经过n次操作后,共删去______ 个小正方形;若要使保留下来的所有小正方形面积之和不超过
,则至少需要操作______ 次.(
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38c5688914317f4a6eef630cba36d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9219bd9c8b266636579b736593279656.png)
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2022-04-21更新
|
1826次组卷
|
9卷引用:湖南省长沙市长郡中学2022届高三下学期高考保温卷(二)数学试题
名校
解题方法
4 . 若在数列的每相邻两项之间插入此两项的积,形成新的数列,再把所得数列按照同样的方法不断构造出新的数列.现对数列1,2进行构造,第一次得到数列1,2,2;第二次得到数列1,2,2,4,2;依次构造,第
次得到的数列的所有项的积记为
,令
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d022a7a5a83884e8bc72aadcce297d.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc321599521a98661ed719cc82ca87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d022a7a5a83884e8bc72aadcce297d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
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2022-04-10更新
|
981次组卷
|
3卷引用:湖南省新高考教学教研联盟2022届高三下学期4月第二次联考数学试题
名校
5 . 已知函数
,若函数
,则函数
的图象的对称中心为______ ;若数列
为等差数列,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c9511d083dde224d944712d875a01d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90930bb1258f4ca110c994153ac5aeb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b431e9f127d083f3c474b43711a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d6eac91a07676df0827896c3c6d678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c9511d083dde224d944712d875a01d.png)
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2022-04-08更新
|
2904次组卷
|
7卷引用:湖南省岳阳市岳阳县2022届高三下学期高考适应性考试数学试题
湖南省岳阳市岳阳县2022届高三下学期高考适应性考试数学试题山东省青岛市2022届三下学期一模数学试题(已下线)数学-2022年高考考前押题密卷(新高考Ⅰ卷)(已下线)2022年高考考前20天终极冲刺攻略(一)【数学】(新高考地区专用)福建省龙岩市上杭县第一中学2022届高三下学期5月模拟考数学试题河北省石家庄市河北正中实验中学2022-2023学年高二下学期开学考试数学试题(已下线)专题1 巧用性质 对称求和【练】
名校
解题方法
6 . 用
表示自然数
的所有正因数中最大的那个奇数,例如:9的正因数有1、3、9,
,10的正因数有1、2、5、10,
.记
,则(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054691f6814632788df468ea28b0c663.png)
______ .(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae5ae56a0293f54c977dee4aaa60368.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e4bbad78eae5d4c694004f33b2ea52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3589cdada38ea373a29824d5306fbf19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9218b28243a6183765b50e588e1dc76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054691f6814632788df468ea28b0c663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae5ae56a0293f54c977dee4aaa60368.png)
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2022-03-18更新
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1232次组卷
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5卷引用:湖南省2022届高三下学期3月调研考试数学试题
7 . 九连环是中国的一种古老智力游戏,它环环相扣,趣味无穷.长期以来,这个益智游戏是数学家及现代电子计算机专家们用于教学研究的课题和例子.中国的末代皇帝溥仪(1906–1967)也曾有一个精美的由九个翡翠缳相连的银制的九连环(如图).现假设有n个圆环,用
表示按某种规则解下n个圆环所需的最小移动次数.已知数列
满足下列条件:
,记
的前项和为
.
![](https://img.xkw.com/dksih/QBM/2022/3/17/2937921792180224/2938953090162688/STEM/92f245bf985c4d418ebcd98e819e3f62.png?resizew=212)
则(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
_______ ;
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb1a7011d92811c6958681b25a14562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://img.xkw.com/dksih/QBM/2022/3/17/2937921792180224/2938953090162688/STEM/92f245bf985c4d418ebcd98e819e3f62.png?resizew=212)
则(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.png)
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名校
8 . 十九世纪法国数学家卢卡斯提出数列
:2,1,3,4,7,…,称之为卢卡斯数列,且满足
,
,
(
),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e60fae499371b1a4de8ef6589276e4d.png)
________ ;记
为数列
的前n项和,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9e39f11663f4782fa114189a7adf99.png)
________ .(以含字母t的代数式表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ab233fde57c65ad8591abac0f6a370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ea0943c8abc65344516556368c4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2668f7b980ccb696a267aea3500edcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9502518f150ee114ffb851b680078069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e60fae499371b1a4de8ef6589276e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ab233fde57c65ad8591abac0f6a370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba6310798cd58e044092647af723689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9e39f11663f4782fa114189a7adf99.png)
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9 . 我国民间剪纸艺术在剪纸时经常会沿纸的某条对称轴把纸对折.现有一张半径为
的圆形纸,对折
次可以得到两个规格相同的图形,将其中之一进行第
次对折后,就会得到三个图形,其中有两个规格相同,取规格相同的两个之一进行第
次对折后,就会得到四个图形,其中依然有两个规格相同,以此类推,每次对折后都会有两个图形规格相同.如果把
次对折后得到的不同规格的图形面积和用
表示,由题意知
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
________ ;如果对折
次,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af67eb6df6db0bccd360595e6bc4838d.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0a9523f2084cf17b8656c11ab1d95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167fa70638432277f8d7af01e665962f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331917350ec33e79e99543eee32eae92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af67eb6df6db0bccd360595e6bc4838d.png)
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2021-11-19更新
|
2541次组卷
|
13卷引用:湖南省株洲市第二中学2023届高三下学期第一次月考数学试题
湖南省株洲市第二中学2023届高三下学期第一次月考数学试题湖南省岳阳市岳阳县2023届高三下学期新高考适应性测试数学试题山东省烟台市2021-2022学年高三上学期期中数学试题江苏省泰州市姜堰中学、如东中学2021-2022学年高三上学期12月阶段性测试数学试题福建省漳州第一中学2022届高三上学期第四次阶段性考试数学试题(已下线)考点25 数列求和及其运用-备战2022年高考数学典型试题解读与变式山东省淄博市淄博实验中学2021-2022学年高三上学期期末数学试题山东省枣庄市2021-2022学年高二上学期期末数学试题(已下线)数学-2022届高三下学期开学摸底考试卷(江苏专用)江苏省盐城市四校2022届高三下学期期初联合检测数学试题宁夏银川市第二中学2022届高三一模数学(理)试题(已下线)二轮拔高卷01-【赢在高考·黄金20卷】备战2022年高考数学模拟卷(新高考专用)(已下线)情境1 关注体育赛事
名校
解题方法
10 . 如图,在一个底面边长为2,侧棱长为
的正四棱锥
中,球
内切于该四棱锥,球
与球
及四棱锥的四个侧面相切,球
与球
及四棱锥的四个侧面相切,
依次作球
与球
及四棱锥的四个侧面相切,则球
的表面积为________ .球
,球
,
,球
的表面积之和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dacb04fa29178c0af4353e4369a7e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800ceb0789a282c65c509e2476a488cc.png)
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