名校
解题方法
1 . 数列
的前
项和为
,则
可以是( )
![](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/32c58093fdb69854da3cb129789def99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599e7f2f8baaa37baa05e1415b790bbb.png)
A.18 | B.12 | C.9 | D.6 |
您最近一年使用:0次
2024-06-12更新
|
1285次组卷
|
5卷引用:浙江省温州市2024届高三第三次适应性考试数学试题
解题方法
2 . 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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名校
解题方法
3 . 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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名校
解题方法
4 . 斜二测画法是一种常用的工程制图方法,在已知图形中平行于
轴的线段,在直观图画成平行于
轴(由
轴顺时针旋转
得到)的线段,且长度为原来的
,平行于
轴的线段不变.如图,在直角坐标系
中,正方形
的边长为
.定义如下图像变换:
表示“将图形用斜二测画法变形后放回原直角坐标系”;
表示“将图形的横坐标保持不变,纵坐标拉伸为原来的
倍”.
经过两次
变换后所得图形为
,求
的坐标;
(2)在第
次复合变换中,将图形先进行一次
变换,再进行一次
变换,
. 记正方形
进行
次复合变换后所得图形为
.过
作
的垂线,垂足为
,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31c9ff64b11c29441ffc10c8cc70cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe33c85f43cc3208ae16c2796b9188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee712dfc82e1acc31ef8dcad479a39.png)
(2)在第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31c9ff64b11c29441ffc10c8cc70cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d904903ab8465eb522d2b8cde0fc29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36134f01da0f13b340e82e8835324f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24172ca004ead2629ef8541a709419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bd7d18f67e90a7c37fad4252e43c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8c8bb5b1ee645a5e94c72823b5f295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-05-08更新
|
823次组卷
|
2卷引用:浙江省杭州学军中学2024届高三下学期4月适应性测试数学试题
名校
解题方法
5 . 已知
是方程
的两根,数列
满足
,
,
.
满足
,其中
. 则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98919b1335a8b7ca020636d1494ad0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073c95775e8c6c15c7f2f8a4a2ad050b.png)
![](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/19a31ae70f96dc4aef6e1ca3ef9fed38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6746bfcdf694447215a11f5b677d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140b5428dace7d41a3967db2f60d633e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c071ed6bc646439b162e096e64fbcd50.png)
A.![]() |
B.![]() |
C.存在实数![]() ![]() ![]() |
D.不存在实数![]() ![]() ![]() |
您最近一年使用:0次
2024-05-08更新
|
952次组卷
|
2卷引用:浙江省杭州学军中学2024届高三下学期4月适应性测试数学试题
6 . 用
表示不超过
的最大整数,已知数列
满足:
,
,
.若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ ;若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c3fdbffff67f73a4f36da898396813.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f9ca737b137a45f33a4cd1d25713c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da849bf4f6c6a1e9d82db5df0392c992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14178ab8fb2a3c405dd1c69e3063512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0518fab92475787a7be0581733eea67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c3fdbffff67f73a4f36da898396813.png)
您最近一年使用:0次
2024-03-14更新
|
953次组卷
|
5卷引用:浙江省强基联盟2024届高三下学期3月联考数学试题
7 . 已知数列
满足
,
,令
.若数列
是公比为2的等比数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26049c107c65a8f023bb81edaca38d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848ef33a5c58f543444fc09d42f29c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-25更新
|
1129次组卷
|
4卷引用:浙江省嘉兴市第一中学2024届高三第一次模拟测试数学试题
浙江省嘉兴市第一中学2024届高三第一次模拟测试数学试题浙江省宁波市慈溪市2024届高三上学期期末测试数学试题(已下线)1.3.2 等比数列的前n项和5种常见考法归类(2)辽宁省沈阳市第一二〇中学2023-2024学年高二下学期第二次质量监测数学试题
名校
解题方法
8 . 对于无穷数列
,给出如下三个性质:①
;②对于任意正整数
,都有
;③对于任意正整数
,存在正整数
,使得
定义:同时满足性质①和②的数列为“s数列”,同时满足性质①和③的数列为“t数列”,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e5501eef9f4c4d559b6a55c3ec922f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4af697f3e81588d213a0741579ab26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1946803973f5d8e0af84cc38b21cffe.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若等比数列![]() ![]() |
您最近一年使用:0次
2024-01-14更新
|
823次组卷
|
3卷引用:浙江省湖州市第二中学2024届高三下学期新高考模拟数学试题
9 . 对于给定的数列
,如果存在实数
,使得
对任意
成立,我们称数列
是“线性数列”,数列
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f078744c54ed52bfd04939b66861f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4d601f95d5d5ea8206d5df9a37f789.png)
A.等差数列是“线性数列” | B.等比数列是“线性数列” |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
2023-11-09更新
|
1233次组卷
|
6卷引用:浙江省金华十校2024届高三上学期11月模拟考试数学试题
浙江省金华十校2024届高三上学期11月模拟考试数学试题(已下线)专题05 数列江西省赣州市全南县全南中学2024届高三上学期期中数学试题安徽省合肥市六校联盟2023-2024学年高二上学期1月期末考试数学试题(已下线)压轴第10题 递推数列问题(一题多变)(已下线)模型1 用综合法快解新情境背景下的数列创新题模型(高中数学模型大归纳)
解题方法
10 . 意大利著名数学家莱昂纳多.斐波那契( Leonardo Fibonacci)在研究兔子繁殖问题时,发现有这样一列数:1,1,2,3,5,8,13,21,34,…,该数列的特点是:前两个数都是1,从第三个数起,每一个数都等于它的前面两个数的和,人们把这样的一列数称为“斐波那契数列”.同时,随着
趋于无穷大,其前一项与后一项的比值越来越逼近黄金分割
,因此又称“黄金分割数列”,记斐波那契数列为
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3feb6b6ef4069134061525264fab958a.png)
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