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1 . 阿基米德螺线广泛存在于自然界中,具有重要作用.如图,在平面直角坐标系
中,螺线与坐标轴依次交于点
,
,
,
,
,
,
,
,并按这样的规律继续下去.给出下列四个结论:
,
为整数;②对于任意正整数
,
为整数;③存在正整数
,三角形
的面积为2025;④存在正整数
,三角形
为锐角三角形.其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17584c9b8f4e48c3a8e0a7c8ac626d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920e36afc62923f2dda82631490fc547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ac934c7b049be27290784a9478c82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1511466ac46376133963f9276381a83b.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2f40d15b6e2e0d09d4f12d4f600e53.png)
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2 . 将
阶数阵
记作
(其中,当且仅当
时,
).如果对于任意的
,当
时,都有
,那么称数阵
具有性质
.
(Ⅰ)写出一个具有性质
的数阵
,满足以下三个条件:①
,②数列
是公差为2的等差数列,③数列
是公比为
的等比数列;
(Ⅱ)将一个具有性质A的数阵
的每一列原有的各数按照从上到下递增的顺序排列,形成一个新的
阶数阵,记作数阵
.试判断数阵
是否具有性质A,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f54b17a7fbf7220c441081faa1b89bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4561d9f0192fefa4fbe13b873870b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e531b92668d0247db929cc5eb43d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8869723ad5015e5124d0f5def782c23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e04de3b82616c97e5292ee36668d7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166db5a2fdd71595bd7e5aedf185dcf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae327610a1b9d6e2f40e086024d4753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4561d9f0192fefa4fbe13b873870b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅰ)写出一个具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d3c740f55aaa7517911b64c10a3df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35aea718ef448f4dd96ff22dca1f9628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f97e878e36da1ad81ae8f90dab5995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dec760cb610a155a4ad7cf6edd01a14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(Ⅱ)将一个具有性质A的数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4561d9f0192fefa4fbe13b873870b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac426c29f630e98c45ecc9a33e2d04b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac426c29f630e98c45ecc9a33e2d04b.png)
您最近一年使用:0次
2019-01-17更新
|
475次组卷
|
2卷引用:【区级联考】北京市丰台区2019届高三第一学期期末考试数学(理)试题
12-13高三上·江苏无锡·期中
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3 . 已知数列
的前
项和
满足
,数列
满足
.
Ⅰ
求数列
和数列
的通项公式;
Ⅱ
令
,若
对于一切的正整数
恒成立,求实数
的取值范围;
Ⅲ
数列
中是否存在
,且
使
,
,
成等差数列?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbcc4d79a9b2b023dd9c3ee5ec06b6b.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875a08b714fe25238bf663de3e190f77.png)
您最近一年使用:0次
2018-12-12更新
|
947次组卷
|
4卷引用:【区级联考】北京市通州区2019届高三上学期期中考试数学(理)试题
【区级联考】北京市通州区2019届高三上学期期中考试数学(理)试题2020届北京市海淀区首都师范大学附属中学高三开学考试数学试题北京市海淀区中关村中学2022届高三上学期开学测试数学试题(已下线)2012届江苏省无锡市高三上学期期中考试数学
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4 . 已知两个半径不等的圆盘叠放在一起(有一轴穿过它们的圆心),两圆盘上分别有互相垂直的两条直径将其分为四个区域,小圆盘上所写的实数分别记为
,大圆盘上所写的实数分别记为
,如图所示.将小圆盘逆时针旋转
次,每次转动
,记
为转动
次后各区域内两数乘积之和,例如
. 若
,
,则以下结论正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7a262d36d4d0f2cae62127aab1bd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751dd6bbc4a89e7dedc586943dfe3299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0468237bbc0d3df77435d98b817c10c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b2c0df4db02a2d66619a5649d1006d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f70fb21e990f9726c9ac662b4f6531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dc116ee4e7f87cbb059c688afe9358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701ce540257c2afe1b5bc92bb1e70a01.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/23/bb391e87-2ba5-4410-88cc-b7058123cbe3.png?resizew=136)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2017-05-08更新
|
811次组卷
|
4卷引用:北京市海淀区2017届高三5月期末练习(二模)数学(理)试题