名校
解题方法
1 . 已知首项为1的数列
的前
项和为
,其中
,现有以下结论:①
;②
;③
.则正确结论的序号为( )
![](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/5de33eee3f30cd929620f7f52069c894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f801629bc14181f7e0cd2aa67c22b527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0eda61a7d9fc046aac897b6073c52b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abf15ab668060c0fc89a73dbfd57d5f.png)
A.① | B.② | C.②③ | D.①②③ |
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名校
解题方法
2 . 已知正项数列
的前
项和
满足
,若
,记
表示不超过
的最大整数,则
( )
![](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/7cde50840989dd1b867658688bccb4bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ab66ea0e62f481d2f0f475023732c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23145dde872b37ef225d66504b43e21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5605641e382f30b9ea5ac5f4a61c19.png)
A.37 | B.38 | C.39 | D.40 |
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3 . 已知数列
的前n项的积为
,
,则使得
成立的n的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f621bcf0de95972ec3e571baf10bb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc25d179aca6dc451fc4e5da700b7280.png)
A.2021 | B.2022 | C.2023 | D.2024 |
您最近一年使用:0次
4 . 在学习完“错位相减法”后,善于观察的同学发现对于“等差
等比数列”此类数列求和,也可以使用“裂项相消法”求解.例如
,故数列
的前n项和
.记数列
的前n项和为
,利用上述方法求
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108d3abd00dbb2332a66411af6bacf4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b7f3d0291da980adfebfa1613ac1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceab1a4ce507465622cecce3d9ff6df1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1034fd9bf38ea74e48c70e697b94d0a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知数列
满足
.记数列
的前n项和为
,则 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7ffb376b02caa2d084beffd26feec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
6 . 已知首项为6的数列
满足
(
,且
),若存在正整数k,使得
成立,则k的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bb2afd094406bfd3ed765873db5715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0489169462e8bb14ebba1c1ae90cd0f.png)
A.7 | B.8 | C.9 | D.10 |
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7 . 已知函数
满足对任意的
且
都有
,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffc8e04902733562565506fb708f9b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21a72ed80a1ac5b802f9a934201e988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a9c4d1ac7ebd56bd164748bb412414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783d006a5a03513906b444cd7c89d84e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-19更新
|
2318次组卷
|
7卷引用:浙江省天域全国名校协作体2023-2024学年高三二模数学试题
浙江省天域全国名校协作体2023-2024学年高三二模数学试题山东省青岛第二中学2024届高三下学期二模考试数学试题(已下线)第16题 抽象函数与数列结合(一题多变)(已下线)压轴题01集合新定义、函数与导数13题型汇总 -1(已下线)【讲】专题10 数列与其它知识的交汇问题(已下线)重难点突破01 抽象函数模型归纳总结(八大题型)辽宁省沈阳市东北育才学校科学高中部2023-2024学年高二下学期期中考试数学试题
解题方法
8 . 如果
,记
为区间
内的所有整数.例如,如果
,则
;如果
,则
或3;如果
,则
不存在.已知
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26039f31af6cacb74636a90ae4df9b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8a094f3cc5dfbcdf2579830faccab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c38da3ff65e3aa467094a04c37979d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5d6a1db57c02d6fa64e9e55fe8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583b10b1050c1de417cf05733d9943f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b174dbab52ccacf8fd89bb156ef025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d88bc255deebebc07d5312cf8c46df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2caedee92c1cb1cadcdb1c7bc0261f.png)
A.36 | B.35 | C.34 | D.33 |
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2024高二下·全国·专题练习
解题方法
9 . 高斯是德国著名数学家,近代数学的奠基者之一,享有“数学王子”的称号,用他名字定义的函数称为高斯函数
,其中
表示不超过
的最大整数,如
,
,已知数列
满足
,
,
,若
,
为数列
的前
项和,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc74f388d1672074d66ca67581388f6c.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/2d54a0e82778f606d95a486835ac9f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f2323cbdf0b1b71092c962ae705102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d845281cd834068104af1b1aa6027c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73c39be7e317460e2fe1d4e05195bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bc88dbf8fc854838ea57a24924d080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c3ac959bdf1b78cb98d92b87c91c46.png)
A.2023 | B.2024 | C.2025 | D.2026 |
您最近一年使用:0次