解题方法
1 . 对于
,将n表示为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc3d9eae90e416ac7bf09a61b5c1011.png)
,当
时,
.当
时,
为0或1.记
为上述表示中
为0的个数,(例如
,
,故
,
).若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc4c2ce6380d1caea0b8beb94d8ef3d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc3d9eae90e416ac7bf09a61b5c1011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24cfa95e7af7b564b57403690024cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1487f4b936e5f924fa6b1ea298e302f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4988a9309359e790f4750d640a615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b9a20da2019c8c6697f365456c1cf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c16dff106bc3e26a1a61c1eaa95460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a536820bedb3b1a47dd74260a4dfdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77c5ac1e6bcee8706774bee5730c91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dfc53dd98d0bbff9c2c64ed08c75ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9eb79cd236e252676052b91d915648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8429564102603b57b24b84c99a341254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc4c2ce6380d1caea0b8beb94d8ef3d.png)
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2023-08-12更新
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6卷引用:上海外国语大学附属浦东外国语学校2022-2023学年高二下学期期中数学试题
上海外国语大学附属浦东外国语学校2022-2023学年高二下学期期中数学试题(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第三册)(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)第05讲 拓展一:数学探究:杨辉三角的性质与应用(知识清单+4类热点题型精讲+强化分层精练)(已下线)高二下学期期中数学试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)
2 . 已知等比数列
,前
项和为
,满足
.
(1)求
的值及
的通项公式;
(2)求
的值;
(3)若数列
满足
,求数列
的前
项和
.
![](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/fe2a7c19ce0b08dbaaa8a90c18929295.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697a6a50f9604ec2b5e597f173bcfc24.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da775220f9e2352d1b953b40f0e0150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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3 . 已知数列
满足:
,设
表示数列
的前n项和.下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d199ece92c41c08b70f934b20c85cea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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名校
解题方法
4 . 已知数列
的前
项和为
,数列
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0868397b59a6cdc475a6dabc9a025e51.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/efbd54f2e8b3a303145cd960bcb448a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0868397b59a6cdc475a6dabc9a025e51.png)
您最近一年使用:0次
5 . 已知数列
为等比数列,其前
项和为
,且
,公比为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614306cc3f34bdee4d5d885b79667645.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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3154e42ce5bee86af29648da9a8e02a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614306cc3f34bdee4d5d885b79667645.png)
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2023-07-03更新
|
938次组卷
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5卷引用:上海市进才中学2022-2023学年高一下学期期末数学试题
上海市进才中学2022-2023学年高一下学期期末数学试题江西省彭泽县第二高级中学2022-2023学年高二下学期7月期末数学试题上海市格致中学2023-2024学年高二下学期期中考试数学试题(已下线)专题01 数列(6大考点经典基础练+优选提升练)-【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(新高考专用)(已下线)上海市高二下学期期末真题必刷02(基础题)--高二期末考点大串讲(沪教版2020选修)
2023高二·全国·专题练习
名校
解题方法
6 . 记
为等比数列
的前n项和,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9ad4e59d7081cf19021423a984bc29.png)
_______ .
![](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/9fc55f38694a72b09eb15027f8c9d8b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a7e8e7b57a40356e959d6690682dfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9ad4e59d7081cf19021423a984bc29.png)
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2023·上海浦东新·模拟预测
名校
解题方法
7 . 已知
,当
时,
是线段
的中点,点
在所有的线段
上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab9fbf074bb0495f7130797464607.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea59ed038abfbff5bc568d184e8463e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039af66355ed85ff4c204931b882b694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d159513efe8dc11305ff2fc3942110a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5d6940ef122dcb071e361c7161c82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab9fbf074bb0495f7130797464607.png)
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22-23高一下·上海浦东新·期末
名校
解题方法
8 . 定义:若对任意正整数n,数列
的前n项和
都为完全平方数,则称数列
为“完全平方数列”;特别地,若存在正整数n,使得数列
的前n项和
为完全平方数,则称数列
为“部分平方数列”.
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c727e96947fc8f6b93572daf14921809.png)
,求证:
为部分平方数列;
(2)若数列
的前n项和
(t是正整数),那么数列
是否为“完全平方数列”?若是,求出t的值;若不是,请说明理由;
(3)试求所有为“完全平方数列”的等差数列的通项公式.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c727e96947fc8f6b93572daf14921809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a516b908d295ad0077ae5e8777a4a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ee9273cc82d57d99a21fb9c4953d46.png)
(3)试求所有为“完全平方数列”的等差数列的通项公式.
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名校
解题方法
9 . 已知数列
的前
项和为
,且
.
(1)求
的通项公式;
(2)求数列
的前
项和
.
![](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/83ee53ebc6c4d311b7a0277e9b05258b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
10 . 若数列
满足
(n为正整数,p为常数),则称数列
为等方差数列,p为公方差.
(1)已知数列
的通项公式分别为
判断上述两个数列是否为等方差数列,并说明理由;
(2)若数列
是首项为1,公方差为2的等方差数列,数列
满足
,且
,求正整数m的值;
(3)在(1)、(2)的条件下,若在
与
之间依次插入数列
中的
项构成新数列
,
,求数列
中前50项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595955aa3a2670abcd60c78a5086f2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56c975b8b3195cea6ef4b9949e5d0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9764763cde4a065aa276c7dbe91773.png)
(2)若数列
![](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/73d4d1ac46eb6cf5f711cdfa8662dd6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a647029ac8d38aba9dda5b94588dcbd4.png)
(3)在(1)、(2)的条件下,若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4741eb4c177d75ca74fe2d36e52ecbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf52946ef832dd2fa7a82dcd6d1bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41806cbde05bd95cc402c702485bd84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50ee5f150f0dbd416e0f8fe9c80ce9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc1e7a87da7751da31f851ae6d46aff.png)
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2023-06-07更新
|
733次组卷
|
3卷引用:上海市进才中学2024届高三上学期开学考试数学试题