1 . 对于数列
,定义“
变换”:
将数列
变换成数列
,其中
,且
.这种“
变换”记作
,继续对数列
进行“
变换”,得到数列
,依此类推,当得到的数列各项均为0时变换结束.
(1)写出数列
,经过6次“
变换”后得到的数列;
(2)若
不全相等,判断数列
经过不断的“
变换”是否会结束,并说明理由;
(3)设数列
经过
次“
变换”得到的数列各项之和最小,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e2d39195e5945c62fc776dcfbb0b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0af5fd5764f190dacd5e924c1af8c74a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f44d6e929223f8bdef1c028f82301e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e374762fa02d95091036d3d4df4e590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a45c538cfbb59c7c8b58dbbfbabf00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81a9ae8e076e39345d58582b8fc21a2.png)
(1)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302499e30cd0bec7e2d6e5826f787766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e61cb2b20a631726c8876182000b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c791be794c2627def012d18bf1f99c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
2 . 已知数列
的前
项和为
,满足
;数列
满足
,其中
.
(1)求数列
的通项公式;
(2)对于给定的正整数
,在
和
之间插入
个数
,使
,
成等差数列.
(i)求
;
(ii)是否存在正整数
,使得
恰好是数列
或
中的项?若存在,求出所有满足条件的
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/83fd67e206753eff52406291c19daa38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23f7f601ad9971d3de3e2dd820642e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0197eeeeaafec6b1fdd7bb8509572f6b.png)
(2)对于给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd6f136f7c8d27b406c0993dcfece54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417083c7157cf0b45befc7c537f1012c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629e172f62f389ea84b7d771c1c27566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a039f1df440117fe89030a4ad6dcf291.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22be6bbf70b5c135edaf8db69118cb50.png)
(ii)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75ed0812322ed46d25ec41f609674be.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/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-03-19更新
|
2008次组卷
|
6卷引用:江西省吉安市第一中学2024届高三下学期期中考试数学试题
名校
解题方法
3 . 已知
是二次函数,且满足
.
(1)求
的解析式.
(2)已知函数
满足以下两个条件:①
的图象恒在
图象的下方;②对任意
恒成立.求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999defcfb0f5662add5a961f536ab59d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359dd4ffb1b26b4cf1fdf582801170b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8979896edfd78d9ae41ee7fba7d9ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a90fb5a4da9ac8e75972f0861fef8a6.png)
您最近一年使用:0次
2022-12-07更新
|
859次组卷
|
3卷引用:江西省南昌市青山湖区南昌大学附中2023-2024学年高一上学期期中数学试题
4 . 如果无穷数列
是等差数列,且满足:①
、
,
,使得
;②
,
、
,使得
,则称数列
是“
数列”.
(1)下列无穷等差数列中,是“
数列”的为___________;(直接写出结论)
、
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
、
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
、
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
、
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
(2)证明:若数列
是“
数列”,则
且公差
;
(3)若数列
是“
数列”且其公差
为常数,求
的所有通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29941e993000d419b14c0d4e925f5b19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b3a3baa88a51e1dbedf37e4d977e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b698f875cfb478d3c601d3de4f71a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93946d0c837a3f1db7fa127218d2ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfda8a67a8d92ec8809c8e76bd7e45a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48d21d10197c3d078db9d1ac9293e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b3a3baa88a51e1dbedf37e4d977e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93946d0c837a3f1db7fa127218d2ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)下列无穷等差数列中,是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b321556cdf2496c22aae75453a52433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09794316b88ac54a4d9e08c57f918346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d313fd69bb1d3007786ab5b48f117b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e1f9a90aaf2ce171f1d89bac40c3016.png)
![](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/aee7bb49247387a9028602315729f8d7.png)
(2)证明:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f350a798b076e55ad197897a9a934a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280a3ac81959ffcd56a4304b61c683b8.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5c65abd6c446e79ea64cdce1bc6834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2022-04-07更新
|
2339次组卷
|
9卷引用:黄金卷03(2024新题型)
(已下线)黄金卷03(2024新题型)北京市西城区2022届高三一模数学试题(已下线)临考押题卷03-2022年高考数学临考押题卷(北京卷)北京市第八中学2023届高三上学期8月测试二数学试题北京市一零一中学2023届高三下学期统练数学试题(一)北京卷专题18数列(解答题)北京市昌平区第二中学2022-2023学年高二下学期期中数学模拟练习试题(已下线)专题5 等差数列的单调性和前n项和的最值问题 微点1 等差数列的单调性北京市第八中学2023-2024学年高二下学期期中练习数学试题
名校
5 . 对于给定的正整数
和实数
,若数列
满足如下两个性质:①
;②对
,
,则称数列
具有性质
.
(1)若数列
具有性质
,求数列
的前
项和;
(2)对于给定的正奇数
,若数列
同时具有性质
和
,求数列
的通项公式;
(3)若数列
具有性质
,求证:存在自然数
,对任意的正整数
,不等式
均成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47831e50ef2d068c6c5874304fd6404c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac657ea5bbf4b237a30e4074c76cc81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6314ea082d345042a5f60044b9da055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dfd181a4137ab8a71da7f9ff815f063.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474e73439b6e497593216e5625610b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
(2)对于给定的正奇数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/197650aa3d6df43e074e656285923e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde821d2523d1cb8928dea513cbf2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dfd181a4137ab8a71da7f9ff815f063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3a0d76c040de0117ed775630b99b10.png)
您最近一年使用:0次
2022-01-12更新
|
1446次组卷
|
9卷引用:江西省新余市第一中学2021-2022学高二年级下学期开学考试数学(理)试题
江西省新余市第一中学2021-2022学高二年级下学期开学考试数学(理)试题北京市东城区2022届高三上学期期末统一检测数学试题(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)北京市怀柔区第一中学2022-2023学年高二下学期期中考试数学试卷北京市东直门中学2024届高三上学期开学考试数学试题上海市复旦大学附属中学2023-2024学年高二上学期阶段性学业水平检测2(暨拓展考试6)数学试题北京市东城区第一六六中学2023-2024学年高二上学期期末模拟数学试题辽宁省辽东南协作体2023-2024学年高三下学期开学考试数学试题北京市北京师范大学附属实验中学2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
6 . 1.设数列
中前两项
、
给定,若对于每个正整数
,均存在正整数
使得
,则称数列
为“
数列”.
(1)若数列
为
、
的等比数列,当
时,试问
与
是否相等,并说明数列
是否为“
数列”﹔
(2)讨论首项为
、公差为
的等差数列
是否为“
数列”,并说明理由;
(3)已知数列
为“
数列”,且
,
,记
,其中正整数
,对于每个正整数
,当正整数
分别取1、2、…、
时,
的最大值记为
,最小值记为
,设
,当正整数
满足
时,比较
与
的大小,并求出
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a22f5023293a85d8381277769d68dc.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/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53c09fba64f3bc86dac3e29bf56b018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b608c12c4e7b9e6d7561be763c6733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a22f5023293a85d8381277769d68dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9dae8e6c9b93458f324f30538a3eb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0055ef3b9c21a572f6cc0a79cdce9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a22f5023293a85d8381277769d68dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)讨论首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07186f6469ba083a12864ddee551246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918893290e48bba154bd5a14a805f10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf57ba4761db4d3fc993ae5815325bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717d039b3a4967ca6b0a899bfd12a83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268b0a589ddfd494ebc898a556c260bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
2021-12-10更新
|
811次组卷
|
4卷引用:江西省安福中学2021-2022学年高二上学期开学考试数学(理)试题
江西省安福中学2021-2022学年高二上学期开学考试数学(理)试题上海市上海师范大学附属中学2020-2021学年高一下学期期末数学试题上海市格致中学2022届高三上学期12月月考数学试题(已下线)专题03 《数列》中的压轴题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
7 . 今有一个“数列过滤器”,它会将进入的无穷非减正整数数列删去某些项,并将剩下的项按原来的位置排好形成一个新的无穷非减正整数数列,每次“过滤”会删去数列中除以
余数为
的项,将这样的操作记为
操作.设数列
是无穷非减正整数数列.
(1)若
,
进行
操作后得到
,设
前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①求
.
②是否存在
,使得
成等差?若存在,求出所有的
;若不存在,说明理由.
(2)若
,对
进行
与
操作得到
,再将
中下标除以4余数为0,1的项删掉最终得到
证明:每个大于1的奇平方数都是
中相邻两项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db096d683f869f67d53bfbc0e759cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd54ff3a3c052b260907774f5ec2e897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983628eb126ac604d4586fdd181d6f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e43291fc522f7e586029d9fe8fc4422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
②是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff319b7da38c9f89f25278f84883dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e726f2fda6ba420750c81041b9275a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616110875a674497c7e2331b872940e6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c75ae8507f8658a01f581715566c96a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ae8420e018bc00b53c8e34cb2c7a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b3f7806d0a60ea224cfeee962bb207.png)
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2020-03-25更新
|
658次组卷
|
5卷引用:江西省全南中学2023-2024学年高二下学期3月月考数学试卷
名校
8 . 已知函数
是奇函数.
(1)求实数
的值;
(2)若
,对任意
有
恒成立,求实数
取值范围;
(3)设
,若
,问是否存在实数
使函数
在
上的最大值为
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f035af9a7f8463d3e9986c470cd507.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa6e9df5ed46e9a0ddba84d4b82813b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce571150e1b70fe3a43e122ee162fe97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8e438779a1055155e15b67798e75ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a98186dcca4e3093a3e910b705b087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66edbe4e1f5d213e3026c81c17ef113d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-11-08更新
|
2473次组卷
|
5卷引用:江西省宜春市宜春中学2023-2024学年高一上学期期末数学试题
名校
9 . 已知数列
的各项均为正值,
对任意
,
都成立.
(1)求数列
、
的通项公式;
(2)令
,求数列
的前
项和
;
(3)当
且
时,证明对任意
都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14f5fdf0e4f9de36f08402dd96d237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8eea2f9029ae4ce8c9348720395c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa51c8baa664d7444153182b7ff5ecb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba590f71638ebfbb77e4c1d7bdb64a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b710eef0f8ef29b9340e6800859a0f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f609d4906415d510ea823a39a64d481e.png)
您最近一年使用:0次
2019-10-02更新
|
1349次组卷
|
4卷引用:江西省新余市第四中学2017-2018学年高二上学期第二次段考数学(理)试题
江西省新余市第四中学2017-2018学年高二上学期第二次段考数学(理)试题江西省宜春市上高县第二中学2019-2020学年高一下学期期末考试数学(理)试题江西省吉安市吉安县第三中学、安福二中2021-2022学年上学期高二入学考试数学试题(已下线)专题11 数列前n项和的求法 微点10 数列前n项和的求法综合训练
名校
10 . 对于无穷数列
,“若存在
,必有
”,则称数列
具有
性质.
(1)若数列
满足
,判断数列
是否具有
性质?是否具有
性质?
(2)对于无穷数列
,设
,求证:若数列
具有
性质,则
必为有限集;
(3)已知
是各项均为正整数的数列,且
既具有
性质,又具有
性质,是否存在正整数
,
,使得
,
,
,…,
,…成等差数列.若存在,请加以证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3cb1321c970c49c9f6a5635ac23d6a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99699ac8106034f647e4f460b3bf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa8264eb8eea3025a152318df8720b1.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e836ef3b31693dcaf25b414277e8ae8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8f894492a8126f5f133dec4cd68833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c414a10d73f453fc1109e5b2243d2369.png)
(2)对于无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926b0a2429ebf269f7e9368ac0306956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e691589e9aafddefcbb613c7030f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知
![](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/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0699adb388000a87241d6b113e733cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969293569368540b9517380795cb571b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfaf6fb5cd9a53f7adc324976735b9a.png)
您最近一年使用:0次
2019-06-18更新
|
1787次组卷
|
5卷引用:江西省吉安市第一中学2024届高三“九省联考”考后适应性测试数学试题(一)
江西省吉安市第一中学2024届高三“九省联考”考后适应性测试数学试题(一)2019年上海市普陀区高三高考三模数学试题广东省湛江市雷州市第二中学2023-2024学年高二下学期开学考试数学试题(已下线)新题型01 新高考新结构二十一大考点汇总-3(已下线)专题06 数列