名校
1 . 已知数列
为有穷数列,且
,若数列
满足如下两个性质,则称数列
为m的k增数列:①
;②对于
,使得
的正整数对
有k个.
(1)写出所有4的1增数列;
(2)当
时,若存在m的6增数列,求m的最小值;
(3)若存在100的k增数列,求k的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c1ee4d7c3f69fdd5a250ab8862d114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9db29473c5e28422317559df73a1037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa768d0bb9bcf827b3e7310e35ef0fbf.png)
(1)写出所有4的1增数列;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
(3)若存在100的k增数列,求k的最大值.
您最近一年使用:0次
2024-03-27更新
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1189次组卷
|
4卷引用:河南省郑州市2024届高三第二次质量预测数学试题
23-24高三上·广东深圳·阶段练习
名校
解题方法
2 . 已知数列
的首项不为0,前
项的和为
,满足
.
(1)证明:
;
(2)若
,证明:
;
(3)是否存在常数
,使得
为等比数列?若存在,求出
的所有可能值;若不存在,说明理由.
![](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/9397a90e4ea953c72b03e20133870979.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4176db941f1af7fcda4ee86c03427f63.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbaa33825e93751c26b463890ac672a.png)
(3)是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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名校
解题方法
3 . 已知无穷数列
的各项均为整数.设数列
的前
项和为
,记
中奇数的个数为
.
(1)若
,试写出数列
的前5项;
(2)证明:“
为奇数,且
为偶数”是“数列
为严格增数列”的充分非必要条件;
(3)若
(
为正整数),求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/41274819307283f0a931fb244401733e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a229173b0f235a4da8aeb6d35f1325f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549d08f011d91ff3f40426a1db0adf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
4 . 已知数列
.设集合
,如果对任意的整数
都有集合
的元素个数等于
,则称
为“完美数列”
(1)分别判断数列
和
是否为“完美数列”,直接写出结论:
(2)若
是“完美数列”,求证:
;
(3)若
是“完美数列”,且
,求出所有满足条件的数列
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d40f91eea8519183dae6bf2af64381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3102d97b673a8c708dde3b6ffbbe2138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c315caff37ae1ebfa412b2adfe130ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)分别判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308f9a69923d8f7347ce5af0fbdb3fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a033921506239df65e3296b1880c7e2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273073906bb7091463fc477b774d49f0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33307fa505efcb8513ef6b6ac45624ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
解题方法
5 . 已知项数为
的数列
是各项均为非负实数的递增数列.若对任意的
,
(
),
与
至少有一个是数列
中的项,则称数列
具有性质
.
(1)判断数列
,
,
,
是否具有性质
,并说明理由;
(2)设数列
具有性质
,求证:
;
(3)若数列
具有性质
,且
不是等差数列,求项数
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc35d18037c40fec3a643a8a0ee1475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/208dfb2f585802ed32c822b6a4005e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f784bc10c59038901c3183b43caccf85.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2022-01-16更新
|
800次组卷
|
3卷引用:北京市朝阳区2021-2022学年高二上学期期末数学试题
北京市朝阳区2021-2022学年高二上学期期末数学试题(已下线)高二数学下学期期末精选50题(压轴版)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)北京市第十七中学2024届高三上学期10月月考数学试题
名校
6 . 已知无穷数列{an}(an∈Z)的前n项和为Sn,记S1,S2,…,Sn中奇数的个数为bn.
(1)若an=n,请写出数列{bn}的前5项;
(2)求证:“a1为奇数,ai(i=2,3,4,…)为偶数”是“数列{bn}是单调递增数列”的充分不必要条件;
(3)若ai=bi,i=1,2,3,…,求数列{an}的通项公式.
(1)若an=n,请写出数列{bn}的前5项;
(2)求证:“a1为奇数,ai(i=2,3,4,…)为偶数”是“数列{bn}是单调递增数列”的充分不必要条件;
(3)若ai=bi,i=1,2,3,…,求数列{an}的通项公式.
您最近一年使用:0次
2019-12-02更新
|
1368次组卷
|
6卷引用:北京市丰台区2018年高三年级一模数学试题(理)
北京市丰台区2018年高三年级一模数学试题(理)北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题上海市育才中学2018-2019学年高三下学期三模数学试卷北京市西城区北京师范大学附中2019-2020学年高二上学期期中数学试题2018年上海市建平中学高考三模数学试题(已下线)专题10 数列通项公式的求法 微点1 观察法(不完全归纳法)、公式法