解题方法
1 . 卷积运算在图象处理、人工智能、通信系统等领域有广泛的应用.一般地,对无穷数列
,
,定义无穷数列
,记作
,称为
与
的卷积.卷积运算有如图所示的直观含义,即
中的项依次为所列数阵从左上角开始各条对角线上元素的和,易知有交换律
.
,
,
,求
,
,
,
;
(2)对
,定义
如下:①当
时,
;②当
时,
为满足通项
的数列
,即将
的每一项向后平移
项,前
项都取为0.试找到数列
,使得
;
(3)若
,
,证明:当
时,
.
![](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/3e30e288d8e1764fde9cf193e2bdc204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf62b0e90a1b3340c00e2a2e1f8ac85.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/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dbbee347cb4a4a531e83a545c5cf306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c99ff3f6386113dbaa7b1e49612da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf62b0e90a1b3340c00e2a2e1f8ac85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fdd7e9cd5d1764bc5de8add15700ae.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79f03f7df0441257dec04bd4ceb0ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b019ff582c6b6f95dc19b4bd4ced254a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca21a96fc2f9f9fab356f81599fc01c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af554aa9625a1c75ad96d9bc3b6c392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b019ff582c6b6f95dc19b4bd4ced254a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4945771db04cd575d385e9355e8a0829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711ca723e111e4db0a70ce4c47ee66d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711ca723e111e4db0a70ce4c47ee66d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8016ef5b66902b71162f20fa0ed02c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6933f66320908d7232fdc92e31bb6123.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf62b0e90a1b3340c00e2a2e1f8ac85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3517fe4fa5b7eeb4878d35ee94a35e.png)
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解题方法
2 . 若正实数数列
满足
,则称
是一个对数凸数列;若实数列
满足
,则称
是一个凸数列.已知
是一个对数凸数列,
.
(1)证明:
;
(2)若
,证明:
;
(3)若
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c162242a938a5a12decf95e793a38bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb56942a7c324e61bf64f45182aac6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010baf415f792018ad9abd752e37b983.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7de869d778679e553d65c8feee7a0b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fae07f950aea5270e6b48fe2cedaaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e44bb3c3c56c02ae33d480b556fece.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e32b345649f33632c83903c6014dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
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3 . 古希腊著名的约瑟夫环问题讲的是:共有127个士兵,围成一个环,从一号位的士兵开始,每个存活下来的人依次杀死相邻的下一位士兵,若一名叫做约瑟夫的士兵想要存活到最后,那么他最开始应当站在几号位上?( )
A.1 | B.63 | C.127 | D.31 |
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4 . 定义:若数列
满足,存在实数M,对任意
,都有
,则称M是数列
的一个上界.现已知
为正项递增数列,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.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/15a8af30dd573218da62ff8c99b99d19.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2023-05-31更新
|
2273次组卷
|
3卷引用:浙江省宁波市镇海中学2023届高三下学期5月模拟考试数学试题
5 . 已知正项数列
,对任意的正整数m、n都有
,则下列结论可能成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4977a59607fe6094fd6a4f39911aac1.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
6 . 已知数列
满足:
,
.记数列
的前
项和为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c467623fabade1d65b370aa9dbee59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 已知数列
满足
,则下列有可能成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1709665198a9a3dfab2f7d671cd4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b01c8ff88fb831a0f9780cf0802d0f.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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8 . 已知向量
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd94a23a224a6af336250d45042d6ba.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f8e88f83024e3e77906a452805c73e.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e2080679ecada053aeb3867327e885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15b6c2de773eb8bb26648f6a0e32f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8610f2ea92d1a8b88969c36d4cc9fd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd94a23a224a6af336250d45042d6ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f8e88f83024e3e77906a452805c73e.png)
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名校
9 . 已知数列
对任意的
,都有
,且
.
①当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2f03f58e3c85de45bd3fd86a8a66f7.png)
_________ .
②若存在
,当
且
为奇数时,
恒为常数P,则P=_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b7776973b6cf7276414eee188abbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326dd1f348f30895419c16f01a17a6ff.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdf53108bee755f5aa9a34ea4d163e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2f03f58e3c85de45bd3fd86a8a66f7.png)
②若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24431f390ba671b4de0d6abaeb9cf476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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2022-03-23更新
|
1711次组卷
|
6卷引用:浙江省强基联盟2022届高三下学期6月统测数学试题二
解题方法
10 . 已知数列
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819d72974cc2440af9a448e5076246a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794dd235c980222337d01626c96371f9.png)
A.对任意的![]() ![]() ![]() |
B.对任意的![]() ![]() ![]() |
C.对任意的![]() ![]() ![]() |
D.对任意的![]() ![]() ![]() |
您最近一年使用:0次
2022-01-03更新
|
1141次组卷
|
5卷引用:浙江省绍兴市诸暨市海亮高级中学2021-2022学年高三上学期12月选考数学试题
浙江省绍兴市诸暨市海亮高级中学2021-2022学年高三上学期12月选考数学试题浙江省绍兴市诸暨市海亮高级中学2022届高三下学期高考前最后一卷数学试题(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-2(已下线)专题9 周期数列 微点2 周期数列的“脸谱”识别(已下线)第4章 数列 章末题型归纳总结(3)