名校
1 . 已知数列
,从中选取第
项、第
项、
、第
项
,若
,则称新数列
为
的长度为m的递增子列.规定:数列
的任意一项都是
的长度为1的递增子列.
(Ⅰ)写出数列
的一个长度为4的递增子列;
(Ⅱ)设数列
.若数列
的长度为p的递增子列中,任意三项均不构成等差数列,求p的最大值;
(Ⅲ)设数列
为等比数列,公比为q,项数为
.判定数列
是否存在长度为3的递增子列:
?若存在,求出N的最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5f59bc23cf55f56312c9ed9806371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af9e7b1c23db5584ad8521d4444d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608d034715f9b1dfb306f9c89d383582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e636879245230dd00a3ab3cbcfbfd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aeb1cbdad3d73306ca2ec905bfe961f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82079a5446d448fb1bea730b968d7e02.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅰ)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33339fa6f26d9c8a9459648af2485e3d.png)
(Ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f86c68104c0f89e3306b37265d6852a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅲ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec57bf360c18a9d0b3d8f89124b1257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a64e9c933af98e51cfeb0113961a88.png)
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2021-01-21更新
|
657次组卷
|
6卷引用:北京市昌平区第一中学2021-2022学年高二下学期期中考试数学试题
2 . (1)已知数列
为等差数列,其前n项和为
.若
,试分别比较
与
、
与
的大小关系.
(2)已知数列
为等差数列,
的前n项和为
.证明:若存在正整数k,使
,则
.
(3)在等比数列
中,设
的前n项乘积
,类比(2)的结论,写出一个与
有关的类似的真命题,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f18f2c2ec67b5e59e4b3d28795d125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b3b63a977f2eb91a87f8eadd3ab078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3549a6c9f727de6be285bcaa281f2f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c2d5971afbff8eca1b9aff5f76f710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f5b63e797195906285c0c03eb9276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05cde56d89850b5e4ba6ee17240b4cd8.png)
(2)已知数列
![](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/e6f18f2c2ec67b5e59e4b3d28795d125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8e90d52301bbdbe6162603db405020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea732c79fa31c37f67e7446a66ec476.png)
(3)在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfa10960d976a70c8b6625cc6451e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5056d12487759b2fe1944612639d39.png)
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