1 . 十九世纪下半叶集合论的创立,奠定了现代数学的基础,著名的“康托三分集”是数学理性思维的构造产物,具有典型的分形特征,其操作过程如下:将闭区间[0,1]均分为三段,去掉中间的区间段
,记为第1次操作;再将剩下的两个区间
,
分别均分为三段,并各自去掉中间的区间段,记为第2次操作...;每次操作都在上一次操作的基础上,将剩下的各个区间分别均分为三段,同样各自去掉中间的区间段:操作过程不断地进行下去,剩下的区间集合即是“康托三分集”,第三次操作后,依次从左到右第三个区间为___________ ,若使前n次操作去掉的所有区间长度之和不小于
,则需要操作的次数n的最小值为____________ .(
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5788219e1b572a03b7453968ad25f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3721aa05c3bf03ee8e92c7fd7a0b48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cba28de35bd3365c48013aa2889a82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c130d40d975aba491541d1a823b509c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f8340ff8ef6994abddab919418423b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0deba532a99234201dd24b23a1b9fc.png)
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2022-05-11更新
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1597次组卷
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4卷引用:山东省德州市2022届高考二模数学试题
山东省德州市2022届高考二模数学试题(已下线)模块八 专题8 以数学文化新情景为背景的压轴题江苏省连云港市赣榆高级中学2022-2023学年高三上学期10月学情检测数学试题(已下线)压轴题03不等式压轴题13题型汇总-2
解题方法
2 . 某数学兴趣小组模仿“杨辉三角”构造了类似的数阵,将一行数列中相邻两项的乘积插入这两项之间,形成下一行数列,以此类推不断得到新的数列.如图,第一行构造数列1,2:第二行得到数列
:第三行得到数列
,则第5行从左数起第8个数的值为___________ ;
表示第
行所有项的乘积,设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d252feb52e1a77b6bac1ba17825095.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2303277c24a13d9f8ef622f841ca6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcc9988fc4a28e8c0379e87b69215ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15222d31df73a231d9436d6e9cbc15a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d252feb52e1a77b6bac1ba17825095.png)
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3 . 如图,某数阵满足:每一行从左到右成等差数列,每一列从上到下成公比相同的等比数列,数阵中各项均为正数,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550427147909013f0491fe8a24d9a5d4.png)
________ ;在数列
中的任意
与
两项之间,都插入
个相同的数
,组成数列
,记数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4331b9fb70a31f8f02b003eea6054c4e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f75e8a3038e0c054a23817196079209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e9bee3a8f1a37ac6c60ae8796027eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550427147909013f0491fe8a24d9a5d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6fd28652117b5c5c61d9032bf78f259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f867d0ca7748f1d788aa81ebaf9bb3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f91e65e0726d85ac43389dc345abda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ea71117a2bf34302a0d2017e1c60e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c75f960d4e68b4405a28cae0eaceda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4331b9fb70a31f8f02b003eea6054c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb936f339f336ed6cc820b803dbd9caf.png)
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4 . 数列
的通项公式为
(n为正整数),其中
表示不超过x的最大整数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fc572cc56fcc7ffd0b9d2d03b0c85f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f32282b8c8366cf2cf1b7304f775be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fc572cc56fcc7ffd0b9d2d03b0c85f.png)
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名校
解题方法
5 . 设
为
的一个排列,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bea2a120d0bb0d28cfaf05e69b465e8.png)
,则这样的排列的个数为_______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fc6113ce4ac2b0daa7b809c9bfb3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed93f368c243d567a5d29ae7b9326ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bea2a120d0bb0d28cfaf05e69b465e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e32c10912f241b6f4da4486a07cf7ac2.png)
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2024-01-14更新
|
561次组卷
|
5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
上海市松江二中2023-2024学年高二上学期期末考试数学试题(已下线)专题01 两个计数原理与排列组合(7类压轴题型)-【常考压轴题】2023-2024学年高二数学压轴题攻略(人教A版2019选择性必修第三册)(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)专题05 计数原理(十七大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
6 . 已知
,数列
为
,规律是在
和
中间插入
项,所有插入的项构成以3为首项,2为公差的等差数列
,则数列
的前30项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aac186947a2ee83597d9949143fd1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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2024-01-02更新
|
772次组卷
|
6卷引用:2024年全国高考名校名师联席命制数学(文)信息卷(七)
(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(七)江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(三)(已下线)考点7 等差、等比数列的联姻 2024届高考数学考点总动员(已下线)高三数学开学摸底考02(新考法,新高考七省地区专用)(已下线)4.2 等比数列(第2课时)(六大题型)(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)压轴题05数列压轴题15题型汇总-1
解题方法
7 . 对于
,将n表示为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc3d9eae90e416ac7bf09a61b5c1011.png)
,当
时,
.当
时,
为0或1.记
为上述表示中
为0的个数,(例如
,
,故
,
).若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc4c2ce6380d1caea0b8beb94d8ef3d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc3d9eae90e416ac7bf09a61b5c1011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24cfa95e7af7b564b57403690024cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1487f4b936e5f924fa6b1ea298e302f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4988a9309359e790f4750d640a615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b9a20da2019c8c6697f365456c1cf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c16dff106bc3e26a1a61c1eaa95460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a536820bedb3b1a47dd74260a4dfdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77c5ac1e6bcee8706774bee5730c91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dfc53dd98d0bbff9c2c64ed08c75ca.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8429564102603b57b24b84c99a341254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc4c2ce6380d1caea0b8beb94d8ef3d.png)
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2023-08-12更新
|
613次组卷
|
6卷引用:上海外国语大学附属浦东外国语学校2022-2023学年高二下学期期中数学试题
上海外国语大学附属浦东外国语学校2022-2023学年高二下学期期中数学试题(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第三册)(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)第05讲 拓展一:数学探究:杨辉三角的性质与应用(知识清单+4类热点题型精讲+强化分层精练)(已下线)高二下学期期中数学试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)
解题方法
8 . 已知数列
为公差不为0的等差数列,
,且
成等比数列,设
表示不超过
的最大整数,如
,记
为数列
的前
项和,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0eecb5b800fce9ae10aed86ffee62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc54335d4de8adc7c8d5425ba9ee67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e91551bb0ae693189ca031f8baa938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb0100a275167c77a1b80cbe01dfc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.png)
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9 . 设数列
是以
为首项,
为公比的等比数列,在
和
之间插入1个数
,使
,
,
成等差数列;在
和
之间插入2个数
,
,使
,
,
,
成等差数列;…;在
和
之间插入n个数
,
,…,
,使
,
,
,…,
,
成等差数列.则
=_______ ;令
,则
=_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/1bcd5c11234a01e2b3d2861e9b3a3aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcd5c11234a01e2b3d2861e9b3a3aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.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/a65cdaa89ae90492504808aba2737fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5733622aabd5a8af1ba76716c86b705a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65cdaa89ae90492504808aba2737fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5733622aabd5a8af1ba76716c86b705a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5cbc4ff3ff76f59867618361b8a2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa76cf9b7e61f025a614dfea37880500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248cbe7c32c92eacf3668e347f07db0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5cbc4ff3ff76f59867618361b8a2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa76cf9b7e61f025a614dfea37880500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248cbe7c32c92eacf3668e347f07db0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5733622aabd5a8af1ba76716c86b705a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87fc39fc53c1603ef8ca571ee8d125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bca9c3219d1a9775734b694a404de1d.png)
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10 . 刺绣是中国优秀的民族传统工艺之一,已经有2000多年的历史.小王同学在刺绣选修课上,设计了一个螺旋形图案--即图中的阴影部分.它的设计方法是:先画一个边长为3的正三角形
,取正三角形
各边的三等分点
,得到第一个阴影三角形
;在正三角形
中,再取各边的三等分点
,得到第二个阴影三角形
;继续依此方法,直到得到图中的螺旋形图案,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1f6745eaaa2fa6474b492536546873.png)
______ ;图中螺旋形图案的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc7fbbecb6a17c04afea9ffe30c3276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bc1d5e8d1a1fbe49c0f0791109caf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dc97d6060d7bdcd077a4803545ec77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bca882264c69f4a7fe06e177713c657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0c74f45b93927d60426c493f2ecba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1f6745eaaa2fa6474b492536546873.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/5f870ee7-5420-417a-8254-65bdda198925.png?resizew=173)
您最近一年使用:0次
2022-05-11更新
|
1194次组卷
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