1 . 已知
为
行
列的数表
,称第
行
列的数
为数表
的一个元素.现给定
中所有元素
,定义
中第
行最大的数与第二大的数(这两数可以相等)的比值为
,第
列的最大数与第二大的数(两数也可以相等)的比值为
,
,记
,由
生成
,同样的方法,由
生成
,
生成
,……为了方便,我们可以把
中的
,
,
记为
,
,
.
表1
表2
(1)若
如表1所示,直接写出
;
(2)证明:
中一定有一行或者一列为1;
(3)若
如表2所示,
,且
,证明:存在
,
中所有元素都为1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39343eb19c5504110501141b5135610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52ab7cfc65e0597ec3aff0080d12f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56b5cc099ff28b2009b7a602b23742c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a20318c91376fd142453b3a7542c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19dd2f5dd5c782fc17b44ad2d68a450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1e4c2eb331b7e9bd77129d9049a940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711a7ead1916052c1ff1f7ddf935b9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826f787ebdcfe55828caf77dd8690b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a20318c91376fd142453b3a7542c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19dd2f5dd5c782fc17b44ad2d68a450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2bd99769042c47a8a709aef1d22a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612877f3243d0df8d514c0501abb6e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9616b76a1e30ab6d4bf92befc896c4b7.png)
1 | 2 | 3 |
6 | 5 | 4 |
1 | 1 | … | 1 |
![]() | ![]() | … | ![]() |
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47a272ba42268bc404ad6d31eabd0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
您最近一年使用:0次
2 . 设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efe6197f4849aca8059c0a9bbf5225.png)
,将
个数
依次放入编号为1,2,…,
的
个位置,得到排列
.将该排列中分别位于奇数与偶数位置的数取出,并按原顺序依次放入对应的前
和后
个位置,得到排列
,将此操作称为C变换,将
分成两段,每段
个数,并对每段作C变换,得到
;当
时,将
分成
段,每段
个数,并对每段C变换,得到
,例如,当
=8时,
,此时
位于
中的第4个位置.
(1)当
=16时,
位于
中的第___ 个位置;
(2)当
(
)时,
位于
中的第___ 个位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efe6197f4849aca8059c0a9bbf5225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e84c08aba58d7695d39e6b4f85acb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f1d912a8e5adc6eb21b301ba7e85b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2a9a08064daadeea0f1acd731053fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f042ab7f9e19baf5cc3c3d605ba9bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabdfa40d74bc127ed1e478b4a253c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fe33ffb69050c0627f8eaba1131fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24879b60db93a877f50cdbd8edf557d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab53ffd5d6034c1722c2502e5d8f2ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb0c78fec78916bbbfca7cc2a4da3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e382c9bafdc5d09498b92f5248d01c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e382c9bafdc5d09498b92f5248d01c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efe6197f4849aca8059c0a9bbf5225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322ba729eb66e803e13fc1dc6f37d7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c438eee3096c6eb60d87c2c98c7c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
您最近一年使用:0次
3 . 分形几何学是数学家伯努瓦·曼得尔布罗在20世纪70年代创立的一门新的数学学科,它的创立为解决传统科学众多领域的难题提供了全新的思路.按照如图甲所示的分形规律可得如图乙所示的一个树形图:记图乙中第
行黑圈的个数为
,则(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
_______ ;(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f982b5f3b4da44ba3fbcfdf507e6d41c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f982b5f3b4da44ba3fbcfdf507e6d41c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/4021e5ca-e1b0-48aa-a758-05f6846b339e.png?resizew=362)
您最近一年使用:0次
名校
4 . 在正整数数列中,由1开始依次按如下规则取到的项:第一次取1;第二次取2个连续的偶数2,4;第三次取3个连续的奇数5,7,9:第四次取4个连续的偶数10,12,14,16……按此规律一直取下去,得到一个子数列1,2,4,5,7,9,10,12,14,16…,则在这个子数列中,第2014个数是( )
A.3965 | B.3966 | C.3968 | D.3969 |
您最近一年使用:0次
5 . 英国数学家泰勒发现了如下公式:
.则下列数值更接近
的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff9bc781c82fc6328909a12cadbd692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd87c578f09b6d397dfdc55cddd8538.png)
A.0.91 | B.0.92 | C.0.93 | D.0.94 |
您最近一年使用:0次
2020-04-06更新
|
692次组卷
|
5卷引用:山东省青岛市黄岛区2019-2020学年高三上学期期中数学试题
山东省青岛市黄岛区2019-2020学年高三上学期期中数学试题湖北省武汉市蔡甸区汉阳一中2020届高三下学期仿真模拟(一)理科数学试题(已下线)专题13 泰勒(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题6-10(已下线)【一题多变】泰勒公式 应用奇特
名校
6 . 观察下面的数表,该表中第6行最后一个数是______ ;设2016是该表的
行第
个数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
![](https://img.xkw.com/dksih/QBM/2020/2/13/2398365623115776/2399339996889088/STEM/32d452942ac743a499b2d79cf9a276da.png?resizew=211)
您最近一年使用:0次
2020-02-15更新
|
275次组卷
|
2卷引用:2019届北京市第五十五中学高三下学期三模数学(文科)试题
名校
7 . 意大利著名数学家斐波那契在研究兔子繁殖问题时,发现有这样一列数:1,1,2,3,5,8,13,21,….该数列的特点是:前两个数都是1,从第三个数起,每一个数都等于它前面两个数的和,人们把这样的一列数组成的数列
称为“斐波那契数列”,则
( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302803ca873cb120a3b8f75dea1c9dab.png)
A.1 | B.2019 | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-10更新
|
697次组卷
|
3卷引用:2020届天津市耀华中学高三年级上学期第二次月考试题
8 . 已知数列1,1,1,2,2,1,2,4,3,1,2,4,8,4,1,2,4,8,16,5,…,其中第一项是
,第二项是1,接着两项为
,
,接着下一项是2,接着三项是
,
,
,接着下一项是3,依此类推.记该数列的前
项和为
,则满足
的最小的正整数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ad4668cc927e277289b2af718f0d91.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/8d536cf2cdf8acc0be66029d3a002c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.65 | B.67 | C.75 | D.77 |
您最近一年使用:0次
2019-11-10更新
|
522次组卷
|
2卷引用:内蒙古自治区赤峰市赤峰二中、呼市二中2019-2020学年高三上学期10月月考数学(理)试题
9 . 观察下列算式:
,
,
,
,…,
,
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e554dd611effa0c913ee20e003f3fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a188596d449f65aa0a9d05a64047700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565e873b3ae4eff30bdcaa660d4f4df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659f45b3c86d71c490e8bcc715ffbeb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c875cd119e75ffabca50e9f569f8efa6.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
您最近一年使用:0次
2019-09-08更新
|
254次组卷
|
2卷引用:江苏省连云港市2018—2019学年度第二学期期末考试高二数学试题(理科)
10 . 已知平面上1个三角形最多把平面分成2个部分,2个三角形最多把平面分成8个部分,3个三角形最多把平面分成20个部分,4个三角形最多把平面分成38个部分,5个三角形最多把平面分成62个部分…,以此类推,平面上
个三角形最多把平面分成 ____________ 个部分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次