解题方法
1 . 已知数列
满足
,
,且
,记数列
的前n项和为
,前n项积为
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b88b469c674cb3d67b08054171a919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.![]() ![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
2 . 高斯是德国著名的数学家,近代数学奠基者之一,享有“数学王子”的称号,他和阿基米德、牛顿并列为世界三大数学家,为了纪念他,人们把函数
称为高斯函数,其中
表示不超过
的最大整数.设
,则
除以2023的余数是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b8b346dd6f878dc915e001674e73d0.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/918fc641eb2c90eb197f08e994d8821b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2023-12-15更新
|
694次组卷
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4卷引用:福建省泉州市普通高中2023-2024学年高二上学期12月学科竞赛数学试题
名校
3 . 已知当
时,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e10245aa9aa362178f8f8cc0ceaf134.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-04-02更新
|
2306次组卷
|
6卷引用:山西省三重教育2023届高三下学期3月联考数学试题
23-24高二上·上海·期末
名校
解题方法
4 . 等差数列
的通项是
,等比数列
满足
,
,其中
,且
、
、
均为正整数.有关数列
,有如下四个命题:
①存在
、
,使得数列
的所有项均在数列
中;
②存在
、
,使得数列
仅有有限项(至少1项)不在数列
中;
③存在
、
,使得数列
的某一项的值为2023;
④存在
、
,使得数列
的前若干项的和为2023.
其中正确的命题个数是( )个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dee512e0fdb19fc03858ce717ce8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e2bbf31fb1a86e83addff6da757cf77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829cf419f1e1f24c133abf13c9297416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c6ce38a0fd768057f68821bac022b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
③存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
④存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
其中正确的命题个数是( )个
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
5 . 已知
是各项均为正数的等比数列,其前n项和为
,
,且
,
,
成等差数列.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
;
(3)设
,
,证明:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c40980226328591a49bf85b56b9562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02b512e23eadd2810ab21e2e993b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3272ce4d31d66c1d408225b997e3a73d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2e7b7b013102caae359e4841f8e7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f275914ae76c22daf8773fc406f0524c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5954dc771c811c8eced9e4c9a19d45ba.png)
您最近一年使用:0次
解题方法
6 . 已知函数
,令
,
,则下列正确的选项为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de0861a5d6af9ca97bed91516bb07cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195fc747e2fc50cb6df2c844d51e4d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85a01f2a5b003d545aabd58658f430.png)
A.数列![]() ![]() ![]() |
B.![]() |
C.若数列![]() ![]() ![]() |
D.![]() |
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解题方法
7 . 已知
为正整数,
.其中
的系数为10,则
的系数的最大可能值与最小可能值之和为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb47fd43ffc4f5d96486ee6126f92c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33e63bee09cf2d57aed06c53ceaf8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
您最近一年使用:0次
2022-07-05更新
|
1441次组卷
|
2卷引用:2022年北京大学强基计划笔试数学试题
8 . 电子计算机是二十世纪最伟大的发明之一,当之无愧地被认为是迄今为止科学和技术所创造的最具影响力的现代工具,被广泛地应用于人们的工作和生活之中,计算机在进行数的计算和处理加工时,内部使用的是二进制计数制,简称二进制.一个十进制数n(n∈N*)可以表示为二进制数(a0a1a2…ak)2,即
,其中a0=1,ai∈{0,1},i=0,1,2,…k,k∈N*,用f(n)表示十进制数n的二进制表示1的个数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d104b50ec3fcb87ec26f71de4bd0d20.png)
A.f(7)=2 |
B.f(7)=3 |
C.对于任意r∈N*,![]() |
D.对于任意r∈N*,![]() |
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解题方法
9 . 已知
为数列
的前n项和,数列
满足
,且
,
是定义在R上的奇函数,且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6ca51105e36446a547b739b1c079b8.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/2815b24f5a89be7ae53aed93182e8988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbc3575e96d9e3969411525624d7092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb7af9e416682c9be1ff154ec3fbfdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6ca51105e36446a547b739b1c079b8.png)
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2022-03-16更新
|
2062次组卷
|
6卷引用:湖北省重点中学沃学联盟2021-2022学年高三上学期期中联考数学试题
名校
解题方法
10 . 已知数列
中,
,且
,设
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db987d0d0025ad2173940bfd9ab95e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f6baaba19c4be5344371e2cb6fcef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6684cf90b338961dc3f9ef8df1f7a53b.png)
A.![]() |
B.数列![]() |
C.![]() |
D.若![]() |
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2021-06-22更新
|
2122次组卷
|
6卷引用:广东省六校2021届第四次联考(深圳市实验学校高中部实验模拟考)数学试题
广东省六校2021届第四次联考(深圳市实验学校高中部实验模拟考)数学试题(已下线)专题7.7 数列前n项和小题(2)-2022届高三数学一轮复习精讲精练(已下线)专题7.7 《数列与数学归纳法》单元测试卷 - 2022年高考数学一轮复习讲练测(新教材新高考)湖北省部分重点中学2022届高三上学期第二次联考数学试题1(已下线)专题08 计数原理(突破训练)-备战2022年高考数学二轮复习重难考点专项突破训练(全国通用)广东省深圳市第七高级中学2022届高三下学期三月月考数学试题