解题方法
1 . 设
,
.如果存在
使得
,那么就说
可被
整除(或
整除
),记做
且称
是
的倍数,
是
的约数(也可称为除数、因数).
不能被
整除就记做
.由整除的定义,不难得出整除的下面几条性质:①若
,
,则
;②
,
互质,若
,
,则
;③若
,则
,其中
.
(1)若数列
满足,
,其前
项和为
,证明:
;
(2)若
为奇数,求证:
能被
整除;
(3)对于整数
与
,
,求证:
可整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72ea8ec0d9f8b1cfc4de834b8bfb608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87803b7cee18366b89d51799250df510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6705dba65746e1d4cac6a268b3c806ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bda3d07c2fef4d6af4a13ade4c743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0601879ae4ca9592246d135bfa48658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383eb235f8e0ceda13367b16d29e0180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503618b9bfb53a06f0ec6a5e427dcdbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da20edf2714109dcfded7e212ec44a.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12059d1dac926a235ccd40c3b61b1b6.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/ed9dbd8ed61db4f1c14f6b0e5f071200.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e4de97f8490fddcff16afe8583266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b96cdd9e003120b6102d927dbf53e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5009ce2d56180d31204f77c871fb375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b326965628b5d967aafe9e696fdc07.png)
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名校
解题方法
2 . 设点集
,从集合
中任取两个不同的点
,
,定义A,
两点间的距离
.
(1)求
中
的点对的个数;
(2)从集合
中任取两个不同的点A,
,用随机变量
表示他们之间的距离
,
①求
的分布列与期望;
②证明:当
足够大时,
.(注:当
足够大时,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3afcb129040d060714f94c0f8c48a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c6d29b3010fc1dc9cb640ad41d5b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8034add7b8011393a866a21479b62f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ffbdfab9dff3ff41ea474f06375032.png)
(2)从集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
②证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59306134d26d7a35fd18bcdd401faeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8eed2b9b1f33517499ef35e044cd104.png)
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7日内更新
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2卷引用:山东省临沂市兰山区等四县区2024届高三第三次模拟考试数学试题
3 . 我们称
元有序实数组
为
维向量,
为该向量的范数,已知
维向量
,其中
,记范数为奇数的
维向量
的个数为
,这
个向量的范数之和为
.
(1)求
和
的值;
(2)求
的值;
(3)当
为偶数时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ed9652852ca4d996fd1f20808df9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a79b7ec77425af9152ef0cd3dacfe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45981f9cd45bf7b0655d3c9e461fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e894b2a2d6b062551e7d16fce65940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6439d5087f29dd37b0627182ba5187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2857fac4963b129d99e79dcb3e13d295.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de9d5e95ba59043c71849a58cd8d061.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953e362ec77e9d5a01ea534385d5a8d4.png)
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名校
解题方法
4 . 某校数学兴趣小组由水平相当的n位同学组成,他们的学号依次为1,2,3,…,n.辅导老师安排一个挑战数学填空题的活动,活动中有两个固定的题,同学们对这两个题轮流作答,每位同学在四分钟内答对第一题及四分钟内答对第二题的概率都为
,每个同学的答题过程都是相互独立的挑战的具体规则如下:
①挑战的同学先做第一题,第一题做对才有机会做第二题;
②挑战按学号由小到大的顺序依次进行,第1号同学开始第1轮挑战;
③若第
号同学在四分钟内未答对第一题,则认为第
轮挑战失败,由第
号同学继续挑战;
④若第
号同学在四分钟内答对了第一题,满四分钟后,辅导老师安排该生答第二题,若该生在四分钟内又答对第二题,则认为挑战成功挑战在第
轮结束;若该生在四分钟内未答对第二题,则也认为第
轮挑战失败,由第
号同学继续挑战;
⑤若挑战进行到了第
轮,则不管第n号同学答对多少题,下轮不再安排同学挑战.
令随机变量
表示n名挑战者在第
轮结束.
(1)求随机变量
的分布列;
(2)若把挑战规则①去掉,换成规则⑥:挑战的同学先做第一题,若有同学在四分钟内答对了第一题,以后挑战的同学不做第一题,直接从第二题开始作答.
令随机变量
表示n名挑战者在第
轮结束.
(ⅰ)求随机变量
的分布列;
(ⅱ)证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
①挑战的同学先做第一题,第一题做对才有机会做第二题;
②挑战按学号由小到大的顺序依次进行,第1号同学开始第1轮挑战;
③若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a004043e329408a50f98d25691ca9652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12444d6e8d3b097a9d090e6ed06042e4.png)
④若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a004043e329408a50f98d25691ca9652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12444d6e8d3b097a9d090e6ed06042e4.png)
⑤若挑战进行到了第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
令随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112f7bd51b9415335f088b7e420d95a9.png)
(1)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad5b0dc4aad791035b5c4ab87bd4702.png)
(2)若把挑战规则①去掉,换成规则⑥:挑战的同学先做第一题,若有同学在四分钟内答对了第一题,以后挑战的同学不做第一题,直接从第二题开始作答.
令随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4cbb3a50014fa18fab2e0de87ee22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1cb18f37c789104e42a4ff4a29a5e7.png)
(ⅰ)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/463ea6a41dfdb38c82925682bd22a0e1.png)
(ⅱ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d12addedfaa3b0740b64b04d0331fe.png)
您最近一年使用:0次
2020-08-06更新
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3054次组卷
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9卷引用:山东省济南市山东省实验中学2024届高三5月针对性考试(二模)数学试题
山东省济南市山东省实验中学2024届高三5月针对性考试(二模)数学试题湖南省长沙市雅礼中学2020届高三下学期高考模拟试卷(二)数学(理)试题湖南省长沙市雅礼中学2020届高三高考数学(理科)模拟试题(一)(a卷)重庆市南开中学2020-2021学年高二下学期3月月考数学试题浙江省杭州市桐庐中学2022-2023学年新高三暑期阶段性测试数学试题(已下线)模块十 计数原理与统计概率-2(已下线)专题26 概率综合问题(分布列)(解答题)(理科)-1(已下线)专题9-1 概率与统计及分布列归类(理)(讲+练)-2湖北省武汉市第十一中学2023-2024学年高二下学期6月考数学试题