名校
1 . 在等差数列
中,若
,则有等式
成立.
类比这一性质,相应地在等比数列
中,若
,则有等式_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fbaaecf683d3158a2d020f2099c873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cd7d7082fada5eeda06ae5b1186688.png)
类比这一性质,相应地在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8dafcd3be708bd03cceb5d62949856.png)
您最近一年使用:0次
2021-02-01更新
|
136次组卷
|
2卷引用:广东省深圳实验学校2020-2021学年高二上学期第二阶段考试数学试题
名校
2 . 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
|
478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)
3 . 定义变换
将平面内的点
变换到平面内的点
;若曲线
经变换
后得到曲线
,曲线
经变换
后得到曲线
,…,依次类推,曲线
经变换
后得到曲线
,当
时,记曲线
与
、
轴正半轴的交点为
和
,某同学研究后认为曲线
具有如下性质:①对任意的
,曲线
都关于原点对称;②对任意的
,曲线
恒过点
;③对任意的
,曲线
均在矩形
(含边界)的内部,其中
的坐标为
;④记矩形
的面积为
,则
;其中所有正确结论的序号是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d819bfb7479b5873f7fa2541697658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d5063a37b8e3e88c7a87267054d407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7959e5d5a687783adf38d2004fd95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc7f40c3bfed77da57b41da844fec1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b25286f6029da66ce5270aacd05184f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51b7bb4deadcb449f0112b7836f59f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd459e842089790c031e4e13695f2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cac997fb53e58edb11f87edd8c6099b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd459e842089790c031e4e13695f2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a63801fa4cfc5d7eb49e443de8be44d.png)
您最近一年使用:0次
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)
您最近一年使用:0次
5 . (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)
您最近一年使用:0次
8-9高二下·辽宁锦州·期末
6 . 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)
您最近一年使用:0次