1 . 两个数列
、
满足
,
,
,
(其中
),则
的通项公式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f2654efba30aab016f41d649af94ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b0dc86922174aa51684cc6eb6aa66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2021-10-29更新
|
2568次组卷
|
10卷引用:江苏省徐州市第一中学2021-2022学年高二上学期10月月考数学试题
江苏省徐州市第一中学2021-2022学年高二上学期10月月考数学试题(已下线)专题4.1 数列 章末检测1(易)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)江苏省常州市前黄高级中学2023届高三考前攀登行动(一)数学试题(已下线)专题15 数列构造求解析式必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)(已下线)专题26 数列的通项公式-5(已下线)数列专题:利用递推关系求通项公式的8种常用方法-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)(已下线)第6讲 数列的通项公式的11种题型总结(4)(已下线)第04讲 数列的通项公式(十六大题型)(讲义)-4(已下线)数列专题:利用递推关系求通项公式(8大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)(已下线)【练】 专题2 构造数列问题
解题方法
2 . 从集合
中取出225个不同的数,组成递增的等差数列,满足要求的数列共有_________ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b363e828f849dbc3f9fd78c392af1401.png)
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3 . 已知两个无穷数列
,
分别满足
,
,其中
,设数列
,
的前n项和分别为
,
.若数列
满足:存在唯一的正整数
,使得
,称数列
为“k坠点数列”.若数列
为“p坠点数列”,数列
为“q坠点数列”,若
,则m的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4989a7c21d25be403b53db197c8ff77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c7fa4d79dd6982e6a9a2c5bb10b707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcb582191f3c4690817af7fe4b5b28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0505b3b01eabf49fa1cd907fe92deb03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0f5c18b7f1fbb05d8d7ab85eeb728c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45a4a72bdca2a17b689b34387e816d8.png)
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解题方法
4 . 对于正整数n,设
是关于x的方程
的实数根.记
,其中
表示不超过x的最大整数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
____________ ;设数列
的前n项和为
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469a49d15c634c79d8e36cb6edaff624.png)
___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2147cdb7c47327b9a8e3274df089aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c84fb3e536f74961243c6b89ddcee09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469a49d15c634c79d8e36cb6edaff624.png)
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2020-08-12更新
|
1973次组卷
|
6卷引用:八省市2021届高三新高考统一适应性考试江苏省无锡市天一中学考前热身模拟数学试题
5 . 已知
,数列
中的每一项均在集合
中,且任意两项不相等,又对于任意的整数
,均有
.记所有满足条件的数列
的个数为
.例如
时,满足条件的数列
为1,2或2,1,所以
.
(1)求
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263faa85998ecb4857b97f40a9fa6e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b28c42df33e1a5fe54b412acb789879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b739e2a6594f3b0c3b5099750062a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28bc1b09a0c1a3fecac62a86c93b85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8876e4e9512be5fbfe5fe4e4fb7527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e96fafcc7b7f783d436f853449208d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
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名校
6 . 设等差数列{an}的公差为d(d≠0),前n项和为Sn.若数列
也是公差为d的等差数列,则数列{an}的通项an=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b48242146203e1dc11e41d54062b8c.png)
您最近一年使用:0次
2020-05-11更新
|
345次组卷
|
2卷引用:江苏省木渎高级中学2020-2021学年高二上学期三校12月联合调研数学试题
7 . 设正整数无穷数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
满足
,
.求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496f9d942ea034a488544eceef6d84c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0748c346ed88f98e424de8edf278325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e359733871dbe3cece59413fa93536b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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8 . 将凸
边形
的边与对角线染上红、蓝两色之一,使得没有三边均为蓝色的三角形. 对
,记
是由顶点
引出的蓝色边的条数.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132df501fe16d9bed7ba8742084baa43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c365eeee68c896623c8a9f4d1a4e0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a89cc62d9ff292fbfc3e1496106892.png)
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9 . 在数列
中,已知
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33faf50aecb1379ea0b5b600549f6c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3b0646a5af210f4d69945c9ea5a0e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e5ec00150c2504b1e06aa64d3f77.png)
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