名校
解题方法
1 . 已知
,数列
的前
项和为
,点
均在函数
的图象上.
(1)求数列
的通项公式;
(2)若
,令
,求数列
的前2024项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa874c2a0f0b2b4e4e4b362a2b548b1c.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5605fe0de6cf73dba5c7cea125ac7107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe1734eeee28524af87e6d01fcbd595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624fb70eac4f5416a2c7d21379e759a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3200f3cc24af2c9663b5c0de282810.png)
您最近一年使用:0次
名校
解题方法
2 . 已知数列
是公比为
的正项等比数列,且
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e15be6eb86b5f1746b0036a87c9ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb6ae18e9f28cbefd073bd6ac0c9e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d787262919c1d297882486899b8f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58117e8491e2af9216622235f2671b5f.png)
A.4050 | B.2025 | C.4052 | D.2026 |
您最近一年使用:0次
3 . 如图为英国生物学家高尔顿设计的“高尔顿板”示意图,每一个黑点代表钉在板上的一颗钉子,下方有从左至右依次编号为
的格子(此时钉子层数为
).当小球从板口下落时,它将碰到钉子并有
的概率向左或向右滚下,继续碰至下一层钓子,依次类推落入底部格子.记小球落入格子的编号为
.定义
.
时
的分布列;
(2)证明:
;
(3)改变格子个数(钉子层数相应改变),进行
次实验,第
且
次实验中向格子最大编号为
的高尔顿板中投入
个小球,记所有实验中所有小球落入的格子编号之和为
.已知无交集的独立事件的期望具有累加性,设每次实验、每次投球相互独立,求
关于
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc67b26dd6f40e0630602168cbc3d784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c2fcac14983abc2b2429936fe0fbb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f1e3925bda80e8223bf7e431585847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5fbb0a0595b5a0153c8b570a6473a0.png)
(3)改变格子个数(钉子层数相应改变),进行
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bd9b00a78632a5355fe47b418996ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efe3b837da0d468d85060c9e0e3b639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/690dd59ae66def0cb99f5bcd3d515e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e77d6f15137ae5d98b0d546672b6f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0bd6753e573bfbe6742d08ef6dfe83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024高三·上海·专题练习
解题方法
4 . 已知函数
,若等比数列
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c647e6ba4d039b599306effdcbf781b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9418beb437753f0bfe9640d3ddf31334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a8bd76e5bf7b62e76143d331cd439.png)
A.2020 | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
5 . 已知
为等差数列,
是公比为2的等比数列.
,且
.
(1)求数列
和
的通项公式;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87199d33ba8ecf0c1af8139ef9838dee.png)
①当
为奇数,求
;
②求
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f40b73b1df3214d091c5e8e5bf52b24c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87199d33ba8ecf0c1af8139ef9838dee.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b6f3489d08e7c44183def51ac4012f.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9bc98588c604cfb47994657fe3bd936.png)
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2024-04-24更新
|
983次组卷
|
2卷引用:天津市八校2023-2024学年高三下学期联合模拟考试数学试题(二)
名校
解题方法
6 . 定义:若对
恒成立,则称数列
为“上凸数列”.
(1)若
,判断
是否为“上凸数列”,如果是,给出证明;如果不是,请说明理由.
(2)若
为“上凸数列”,则当
时,
.
(ⅰ)若数列
为
的前
项和,证明:
;
(ⅱ)对于任意正整数序列
(
为常数且
),若
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e587fa47050e45101bbfbfe129fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3adcc926ce1056eefbad88408820424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48407f815d07eb8b5dfa8d34b724512e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede85acd5056e2907a48131e71c45411.png)
(ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/0a62e059e03eda6884da213547097ed9.png)
(ⅱ)对于任意正整数序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6f1287d0218a833f34a97a9db24cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e988e0b43c5730e1c104004514801d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c9507d571eb0de009f16f1837579f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-04-10更新
|
702次组卷
|
4卷引用:安徽省池州市第一中学2024届高三第一次模拟联合检测数学试题
安徽省池州市第一中学2024届高三第一次模拟联合检测数学试题(已下线)压轴题05数列压轴题15题型汇总-1山东师范大学附属中学2024届高三下学期考前适应性测试数学试题福建省漳州市龙文区2024届高三6月模拟预测数学试题
7 . 已知数列
满足:
,数列
满足
.
(1)求数列
的通项公式;
(2)求
的值;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2ad952b2297d7467bab9013a4a071a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b0b2668db49873d6c3bdf9c2ab6c1d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e06a5664af18f5ea087801b93088877.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1242a2b940ec2104f4280710521ab9a.png)
您最近一年使用:0次
8 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9923045505b26b5a1ef59f3500aea03.png)
,其中
是
上的奇函数,则数列
的通项公式为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9923045505b26b5a1ef59f3500aea03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be613fff0421d9be9e8bb5eb8b07c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64714c73195437d2b6bddeedbd11e82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
9 . 函数
,则
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5d2b464427f13a5b8f458bc09ce5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f29be96f2122939fe605813f2f3e9276.png)
A.2012 | B.![]() | C.2013 | D.![]() |
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|
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4卷引用:第九届高一试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
第九届高一试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)云南省文山州砚山县第三高级中学2023-2024学年高二下学期4月半月考数学试卷 (已下线)第一章数列章末十六种常考题型归类(3)(已下线)专题07 数列通项公式与数列求和--高二期末考点大串讲(人教B版2019选择性必修第三册)
10 . 已知函数
满足
,数列
满足:
.
(1)求数列
的通项公式;
(2)数列
满足
,其前
项和为
,若
对任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f47a8dbff3f06c502f370e6961106da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b209230761fa07f63e4300b7f029429d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd2b2b1c9c82997b28888cef839e67b.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/27c93c6fb7f0a29fee41862aa7604470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c46b33730f3a29b9ec3024df71375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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|
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4卷引用:福建省龙岩市2023-2024学年高二上学期期末教学质量检查数学试题
福建省龙岩市2023-2024学年高二上学期期末教学质量检查数学试题四川省天府新区实外高级中学2023-2024学年高二下学期3月月考数学试卷(已下线)第一章数列章末十六种常考题型归类(3)(已下线)专题04数列求和的6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)