1 . 对正常数
,若无穷数列
,
满足:对任意的
,均有
,则称数列
与
具有“
”关系.
(1)若无穷数列
,
的通项公式分别是
,
,判断数列
与
是否具有“3”关系;
(2)若无穷数列
,
是公差不相等的两个等差数列,对任意正常数
,证明:数列
与
不具有“
”关系;
(3)设无穷数列
是公差为
的等差数列,无穷数列
是首项为正数,公比为
的等比数列,试求“存在正常数
,使得数列
与
具有‘
’关系”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe4fffc64388e7786db703139b43f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87cd7e9a204a619f2f612c94a2b5228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcbbe506132e03ad7962e201a0b0b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)若无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc59f584f053eb2d07b6f51d8a6a7e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c5d989f80848fb13b61fa877de0752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
2 . 已知有限数列
,若满足
,n是项数,则称
满足性质
.
(1)判断数列3,2,5,1和4,3,2,5,1是否具有性质
,请说明理由;
(2)若数列
是
,公比为
的等比数列,项数为10,且具有性质
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c5ae4ee4d5c10f5dfc7bf775270721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(1)判断数列3,2,5,1和4,3,2,5,1是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
您最近一年使用:0次
名校
3 . 记实数
、
中较小者为
,例如
,
,对于无穷数列
,记
.若对任意
均有
,则称数列
为“趋向递增数列”.
(1)已知数列
、
的通项公式分别为
,
,判断数列
、
是否为“趋向递增数列”?并说明理由;
(2)已知首项为
,公比为
的等比数列
是“趋向递增数列”,求公比
的取值范围;
(3)若数列
满足
、
为正实数,且
,求证:数列
为“趋向递增数列”的必要非充分条件是
中没有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6323f3d42a8c329f1231a4183cca21c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d009da28dbbec2e0493e504b153d5e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467d1e5a0787b9a3d892291abc5216a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70642e7d9ccc8591908f12eea59c9daa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34916ec3b585a5926485d45191591e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](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/ccbb83894b8870017f24b5649ddc6360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4412c62615c55a6f09fcd4d54b10488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d42b37737d111c9e40136a4aa3266f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
您最近一年使用:0次
2022-11-06更新
|
1459次组卷
|
8卷引用:上海市徐汇区2022届高三下学期二模数学试题
上海市徐汇区2022届高三下学期二模数学试题(已下线)第10讲 数学归纳法与数列综合应用 - 1(已下线)专题1 数学归纳法及其变种 微点3 数学归纳法综合训练(已下线)模块九 数列-2(已下线)专题8 等比数列的单调性 微点1 判断等比数列单调性的方法(已下线)专题06数列必考题型分类训练-3上海市复旦大学附属中学2022-2023学年高二上学期期末数学试题(已下线)核心考点06数列-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
4 . 已知数列
:
,
,…,
,其中
是给定的正整数,且
.令
,
,
,
,
,
.这里,
表示括号中各数的最大值,
表示括号中各数的最小值.
(1)若数列
:2,0,2,1,-4,2,求
,
的值;
(2)若数列
是首项为1,公比为
的等比数列,且
,求
的值;
(3)若数列
是公差
的等差数列,数列
是数列
中所有项的一个排列,求
的所有可能值(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f766fe39702fecd2b6c21855757907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33527f5f2178a3e7eb7df6cc0a676b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a146d1ac165f167e593bf6b03933e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0ce19d6ffec84ee7334568e933a95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d841396c105ff03a35898d4b96587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a146d1ac165f167e593bf6b03933e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fd8291ffa0740c3f6d0233cd3a5568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0b65265063085f628e232c2c2a8338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9626c69b9ef5db5e22540c404c4a6f.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30072a9cd1d03b6cf2c62c85df63d940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1724a17ff17abe389c4decf0b5e7bd8c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c8f394783e3687c602c7099cd420c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3012337aa392709349731fb1eef5b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92a355bfe012a120d10f677002922c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-05-06更新
|
1594次组卷
|
6卷引用:北京市西城区2022届高三二模数学试题
北京市西城区2022届高三二模数学试题(已下线)2022年新高考北京数学高考真题变式题13-15题北京市第九中学2022届高三下学期保温考试数学试题(已下线)重难点08 七种数列数学思想方法-1(已下线)2022年新高考北京数学高考真题变式题19-21题(已下线)北京市西城区2022届高三二模数学试题变式题16-21
5 . 记实数
,
中的较大者为
,例如
,
,对于无穷数列
,记
,若对于任意的
,均有
,则称数列
为“趋势递减数列”.
(1)已知数列
的通项公式分别为
,
,判断数列
是否为“趋势递减数列”,并说明理由;
(2)已知首项为
公比为
的等比数列
是“趋势递减数列”,求
的取值范围;
(3)若数列
满足
,
为正实数,且
,求证:
为“趋势递减数列”的充要条件为
的项中没有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ff5bb0fe6702b7d57492e82dabc3e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c633c4d52075cb924e6e311d121b829c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c218d14281906e19cfadd586d1f23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175faa34d8fc79072c97fe2665a0b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d61cf95a6aa06636278be1069888b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d789500bdc2144b75c29e4fd28374ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492d0ca5ecaafcb665967f08e1af87aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62f5b4e6d475e233cc30238667b4bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b7716b4e1271cc80c63a38e56446ad.png)
(2)已知首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c84bc401cb7e5a4b0bc1157e5dbd194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4077480b54eb99a86b2bc4fb165b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21098099da24af151a1337ec0754bcd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4077480b54eb99a86b2bc4fb165b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4077480b54eb99a86b2bc4fb165b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
您最近一年使用:0次
6 . 已知数列
与
满足
,
.
(1)若
,求数列
的通项公式;
(2)若
,且数列
是公比等于2的等比数列,求
的值,使数列
也是等比数列;
(3)若
,且
,数列
有最大值
与最小值
,求
的取值范围.
![](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/998926638c7b8a50714455fb2c81693b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10226aabc54614cdc01a68b1a60a5770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078a5f2f480f345ecc5a13bd09ce539f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d96beb63c117094ca155b15c72ac28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de524a163912682710d2a1918d66ff40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467f61f8d38c71fcb30f3f16d88650d7.png)
您最近一年使用:0次
2020-02-08更新
|
429次组卷
|
2卷引用:2016届上海市崇明县高三第二次高考模拟(文)数学试题