名校
1 . 设集合X是实数集R的子集,如果实数
满足:对任意
,都存在
,使得
成立,那么称
为集合X的聚点.则下列集合中,0为该集合的聚点的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd9b15b5cdf1c131ebf7cf2776cf7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c80250b3063d20622071a53e86b77a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
A.![]() | B.![]() |
C.![]() | D.整数集Z |
您最近一年使用:0次
2021-10-07更新
|
998次组卷
|
7卷引用:重庆市西南大学附属中学2021-2022学年高一上学期9月第一次定时训练数学试题
名校
解题方法
2 . 已知
,数列
的前
项和为
,且
;
(1)求证:数列
是等比数列,并求出通项公式;
(2)对于任意的
(其中
,
,
,
均为正整数),若
和
的所有的乘积
的和记为
,试求
的值;
(3)设
,
,若数列
的前
项和为
,是否存在这样的实数
,使得对于所有的
都有
成立?若存在,求出
的取值范围;若不存在,请说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/2e654568f7561197af8dac889750a86b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50e50fee3065db29df0a182e17b9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f01cfc245e926581bdb125e0fba733.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/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb853c35a7d17396aa032e33505002f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeee42a40351adbd5d9445133f0fddfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1c0849b21a1801dd16c74bb491b02b.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6cd8e0e45cfcc1b7305d106e0006bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f69d56ee486f8b7aa15fec31032654.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/edd6a506c0a4d15847ac3fc88437908a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb583e4bd8b09dead61adfcc29740a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
3 . 已知
,函数
的图像与y轴相交于点
,与函数
的图像相交于点
,
,的面积为
,(O为坐标原点),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6eb2fcf76cd58f6573a059ab1ab48b4.png)
____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edec660383c08c26ff438d1b8c7a3177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc7529df978fe3feafd24b6ade74955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd2a7b6e796d8a0d5b18c316ff638bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75e563a1219cc5b71503a618ecfb7d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6eb2fcf76cd58f6573a059ab1ab48b4.png)
您最近一年使用:0次
4 . 在平面直角坐标系中,函数
在第一象限内的图像如图所示,试做如下操作,把
轴上的区间
等分成
个小区间,在每一个小区间上作一个小矩形,使矩形的右端点落在函数
的图像上.若用
,表示第
个矩形的面积,
表示这
个矩形的面积总和.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/9d236159-b191-4908-8623-a647c6a3c36c.png?resizew=144)
(Ⅰ)求
的表达式;
(Ⅱ)请用数学归纳法证明等式:
;
(Ⅲ)求
的值,并说明
的几何意义.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff65953311c700ffe160fb0d8a1afc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff65953311c700ffe160fb0d8a1afc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5742a858aae33282f10a20f60a70498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/9d236159-b191-4908-8623-a647c6a3c36c.png?resizew=144)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
(Ⅱ)请用数学归纳法证明等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d890a201846c41fc9935565d0cce73.png)
(Ⅲ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58abe92020722722506c7b12c7879ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58abe92020722722506c7b12c7879ac5.png)
您最近一年使用:0次
2020-06-03更新
|
283次组卷
|
4卷引用:安徽省蚌埠市第三中学2020-2021学年高二下学期4月月考理科数学试题
解题方法
5 . 按照如下规则构造数表:第一行是:2;第二行是:
;即3,5,第三行是:
即4,6,6,8;
(即从第二行起将上一行的数的每一项各项加1写出,再各项加3写出)
2
3,5
4,6,6,8
5,7,7,9,7,9,9,11
……………………………………
若第
行所有的项的和为
.
(1)求
;
(2)试求
与
的递推关系,并据此求出数列
的通项公式;
(3)设
,求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63aa52c750f39eb315da59ebae171576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb4d826021241482742685f8f68e811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
2
3,5
4,6,6,8
5,7,7,9,7,9,9,11
……………………………………
若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56f8a9f14dab4bd061ac817a39141be.png)
(2)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1bb1af3ce1ba0b5cac2e2916da8e6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58abe92020722722506c7b12c7879ac5.png)
您最近一年使用:0次
2020-02-10更新
|
280次组卷
|
3卷引用:上海市高桥中学2022届高三上学期9月月考数学试题