名校
解题方法
1 . 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x的最大整数. 已知:
,(
,
)
,
,
,求
的值;
(2)若
,
,
,求证:
;
(3)设
,求S除以2023的余数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b7f26fe1977bda9de200debe99f020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851eae00e3369068e33a7e6420483883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2382ddc29a4fec13b4d0a11deb2cfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d290a4927c50661098e2fbea58d77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0956ed974bee14fffcf9ada9cafe49d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964a54ca7774d6fc04aaf8b85fda5fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ee581ca3282490206a8bc11dfb5ccf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a45b5fe1fea8e19026d491596392fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54e945ef81cf9c9d985aa6f2f72dc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1972a6ab2655f4cb706f7dd379902a87.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03304e01039bd5039d463207d81ce65.png)
您最近一年使用:0次
名校
2 . 已知集合
,规定:若集合
,则称
为集合
的一个分拆,当且仅当:
,
,…,
时,
与
为同一分拆,所有不同的分拆种数记为
.例如:当
,
时,集合
的所有分拆为:
,
,
,即
.
(1)求
;
(2)试用
、
表示
;
(3)设
,规定
,证明:当
时,
与
同为奇数或者同为偶数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb813e225b094c636d38d0e0cfbd67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea40e6c6055a63e7934f614e878940ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d114f15fa1bab95c647f87cedab26b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c3c3b06e4d829c5967bd76ab3d14ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623ff4c4d26a22d8ab9e6a70cadf6623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28faa23f36fcfc2aef9cc68f46b1c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d114f15fa1bab95c647f87cedab26b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdc216147253ff9697788764dc1ab93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8a97f873310fac16b20d730f7c4e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a871a43ca9e77e26f5c6b680c165e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b704d8979f50009bcb3ec36a07864d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1fdd193767192adc5adcd772ae2b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da1c8d2d0ddab6eed4da334b0446849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a045201f479d99c868e5bac5632b211.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe036f3bc2712beea23557116fdac74c.png)
(2)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8a97f873310fac16b20d730f7c4e29.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9acc25eced79e4d6973d2edeb5628c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ba78808895f5e4bd393fe7aa5b9a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bb215f28e5eea7ff4c7ca5ee9e2216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-02-07更新
|
1135次组卷
|
8卷引用:期中考试押题卷(考试范围:第6-7章)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)
(已下线)期中考试押题卷(考试范围:第6-7章)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)上海市实验学校2022-2023学年高二上学期期末数学试题(已下线)6.5二项式定理(分层练习)-2022-2023学年高二数学同步精品课堂(沪教版2020选择性必修第二册)(已下线)第6章 计数原理(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(沪教版2020选择性必修第二册)(已下线)第6章 计数原理(基础、常考、易错、压轴)分类专项训练-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)(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)单元测试B卷——第六章 计数原理
名校
3 . 已知数列
的首项为1,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2711dcec2b499c0a8a7481fe0a301ef6.png)
.
(1)若数列
是公比为3的等比数列,求
的值;
(2)若数列
是公差为2的等差数列,①求证:
;②求证:
是关于
的一次多项式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2711dcec2b499c0a8a7481fe0a301ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec0637a42313e1914a6fb1cadf1afda4.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d2775b6bd0885b697afb4209993fa.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2fc1d897837062f069747d9de5c88f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a95cb9161333c191b3e33d76139ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2021-04-23更新
|
670次组卷
|
3卷引用:江苏省苏州十中、三中2020-2021学年高二下学期期中数学试题
名校
4 . (1)设
为虚数单位,求
的实部;
(2)计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18abfd9441f24a5fbd1b7e7d5cd1aab.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e71d0503b3feda569aeeb1036876d9c.png)
您最近一年使用:0次
2021-01-26更新
|
775次组卷
|
2卷引用:江苏省扬州中学2020-2021学年高一(早培)下学期期中数学试题
名校
5 . (1)已知
,求
的值.
(2)已知
的展开式中,各项的系数和比各项的二项式系数和大992.求展开式中系数最大的项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2dcbe0bdfce1a528e71e86a2931c2a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6c07cbfbfd1d255399cdfdb62d301be.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7ae0bd0ce0892d96bf9ebb9f02126f.png)
您最近一年使用:0次
6 . 对于给定的函数
,定义如下:
其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c7aab4df25884973273efae244f2df.png)
(1)当
时,求证:
;
(2)当
时,比较
与
的大小
(3)当
时,求
的不为
的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729065c88ccb1ca1071319a4dfb04fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c7aab4df25884973273efae244f2df.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5d30d6d24314d9d2925cdc33b04815.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bfbf2be4f1b96be108b9c1b7e82262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed70ca50c63a55128f61af3e3ac8f453.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
您最近一年使用:0次