1 . 已知递增数列
的前n项和为
,且
,
.
(1)求数列
的通项公式;
(2)设
.
(ⅰ)求数列
的通项公式;
(ⅱ)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84c2e4a2a86ffc252955c06e9b567e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37b430b94a1afdb43f2a80782627c02.png)
(ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3d151cbe277608d3a6cfbbe3f5eb9a.png)
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解题方法
2 . 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)
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解题方法
3 . 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
4 . 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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5 . 对于三次函数
,给出定义:设
是函数
的导数,
是函数
的导数,若方程
有实数解
,则称点
为函数
的“拐点”.某同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且“拐点”就是对称中心.给定函数
,请你根据上面的探究结果,解答以下问题:
①函数
的对称中心坐标为______ ;
②计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634577ca265c60d146b9d28661e24c4b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db46d62d4c778babb46a0a3d223384e5.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db46d62d4c778babb46a0a3d223384e5.png)
②计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634577ca265c60d146b9d28661e24c4b.png)
您最近一年使用:0次
2024-05-06更新
|
332次组卷
|
2卷引用:江苏省无锡市锡东高级中学2023-2024学年高二下学期期中考试数学试题
名校
解题方法
6 . 已知正项数列
是公比不等于1的等比数列,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff127c5894dccde5d13225154c65063.png)
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46252ac070020798942480959f648153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34992c6184a8e5a1831221ef4aa9f1f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff127c5894dccde5d13225154c65063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2809995903ff16ec696de6d4c761c7e.png)
A.2020 | B.4046 | C.2023 | D.4038 |
您最近一年使用:0次
7 . 已知
,
,则数列
的通项公式为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dfa189d5b6d60f5163dc8bf41ad699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39028143d8a03c695f007d32691ce074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024高三·上海·专题练习
解题方法
8 . 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
9 . 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
|
980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
10 . 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
|
684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