名校
1 . “已知数列
为等差数列,它的前
项和为
,若存在正整数
,使得
,则
”,类比上述结论,若正项数列
为等比数列,__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/b563e90a939ede2d986698f997369212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31fa241aa355a70708f6caaee10de675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22652b7d4adb788bd7a33187f870e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
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名校
2 . 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)
您最近一年使用:0次
2021-01-21更新
|
657次组卷
|
6卷引用:北京市昌平区2021届高三年级上学期期末质量抽测数学试题
名校
3 . 已知数列
满足:对任意
,若
,则
,且
,设
,集合
中元素的最小值记为
;集合
,集合
中元素最小值记为
.
(1)对于数列:
,求
,
;
(2)求证:
;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5897fd42e01b077fe8685e7b7a71e278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfbc054e041fa0b53feb9b81a4608347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7aad65e4222bcab9f6ddc94ea495de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f8fdbba79ddbc156bbb300b1b051e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fd79d9aa9740d095affe36788e01cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a1493a001b60b0e94e342d428caa.png)
(1)对于数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3cf64aad412f59d047c97efa1516175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a1493a001b60b0e94e342d428caa.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aa00523d3ab546ab459d1fff0a6136.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
您最近一年使用:0次
2020-06-13更新
|
479次组卷
|
4卷引用:2020届上海市七宝中学高三三模数学试题
2020届上海市七宝中学高三三模数学试题上海市七宝中学2020届高三下学期模拟数学试题(已下线)卷11-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)(已下线)考向29 推理与证明-备战2022年高考数学一轮复习考点微专题(上海专用)
15-16高一下·上海浦东新·期末
名校
4 . 在等差数列
中,若
,
,则有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296242329f9577e418d43e7d2aa5c906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3467ee10f5edc71b6fb6c55c2640b38.png)
,对于等比数列
,请你写出相应的命题:________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f3561d66962b06ed658fb468329b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28af5c69a5a3d2684cb21a97f2245cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296242329f9577e418d43e7d2aa5c906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3467ee10f5edc71b6fb6c55c2640b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea11312557b36013c3ee180d91adcc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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8-9高二下·辽宁锦州·期末
5 . 在等差数列
中,有
,其中
分别是
的前
项和,用类比推理的方法,在等比数列
中,有________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0242e98ae52be08247a7cd2bafd806d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057ff2c35d2bbe68dcb65f5786b631f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f361cfa414b52679ba2b700d809b090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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