1 . 如图所示数阵,第
行共有
个数,第
行的第1个数为
,第2个数为
,第
个数为
.规定:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c97394c9634fde6e772872b54b6249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f195253d3a2bc6383233e3515903c5b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0991d363c974fad83457c6a78b0152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ce15fa76fda687b1c1fbdc2480c524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497e4a4975dd419a1c65724385950c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34607bb95c84c3bd775c144255895f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
(1)试判断每一行的最后两个数的大小关系,并证明你的结论;
(2)求证:每一行的所在数之和等于下一行的最后一个数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c15166e2227c8c8582bc17f818fa43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29a285201fd7e0ad70fa7431cb89a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0749c4129afc0c704155f522290b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222268dda9dcb9b660f3cbedbb37757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f1e3925bda80e8223bf7e431585847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b344ab26012e4cc663266f04dd700cbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c97394c9634fde6e772872b54b6249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ce266899f72edea3187f4857b802ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d3bec9b8bdeca73764d9d2eb2c0a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f195253d3a2bc6383233e3515903c5b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89299ff7b560424509825ce7c690c5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcad334979e1fa0bef47d84c3c3c101a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fc7959cf1daf71f15861bc4704b111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0991d363c974fad83457c6a78b0152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db1e5ed0e2b01da100e896189c6312d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ee0101530cdc106c05caca4b7014ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c68792cc182e16074dfeaa1bbc7e166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d405be4f523f33ffc67f0d67c129cb7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ce15fa76fda687b1c1fbdc2480c524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9851d400de384cb46bbefdbfc8cdd3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f159ced7d6594cc3d4f7a88fd9bc4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332ab3261e4e33b0948263ba058dc147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d450cef132b9dec887ecd711de4603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a71f2064dc04af9382d1ef31feb0d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497e4a4975dd419a1c65724385950c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785606cbba01206e9d91cb3e6d4d2ab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40e77f739724cbfb3bdfd17ba44e238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df9830c93a2b4e7350544ffd662b82d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6585c61fd9ef5eaa86493b7c65ef581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace8be106f1402565ea778f0818bda9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb5c42bd7166ff6486b3b69ba1e1d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34607bb95c84c3bd775c144255895f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
(1)试判断每一行的最后两个数的大小关系,并证明你的结论;
(2)求证:每一行的所在数之和等于下一行的最后一个数;
您最近一年使用:0次
解题方法
2 . 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)
您最近一年使用:0次
3 . 在机器学习中,精确率
、召回率
、卡帕系数
是衡量算法性能的重要指标.科研机构为了测试某型号扫雷机器人的检测效果,将模拟战场分为100个位点,并在部分位点部署地雷.扫雷机器人依次对每个位点进行检测,
表示事件“选到的位点实际有雷”,
表示事件“选到的位点检测到有雷”,定义:精确率
,召回率
,卡帕系数
,其中
.
(1)若某次测试的结果如下表所示,求该扫雷机器人的精确率
和召回率
.
(2)对任意一次测试,证明:
.
(3)若
,则认为机器人的检测效果良好;若
,则认为检测效果一般;若
,则认为检测效果差.根据卡帕系数
评价(1)中机器人的检测效果.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035744497a9eb070b633d78e5a2973ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c150fe2837b2d6a191e77fcc4fd984d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016078f7e8096746515b68f3d88e6edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999bf73a3e99b33a7dc9e27605f13ea.png)
(1)若某次测试的结果如下表所示,求该扫雷机器人的精确率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
实际有雷 | 实际无雷 | 总计 | |
检测到有雷 | 40 | 24 | 64 |
检测到无雷 | 10 | 26 | 36 |
总计 | 50 | 50 | 100 |
(2)对任意一次测试,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e8b6a9cfa7a1f79de242e13701a8d2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326127fdb2c7118ad2c942704c35bf89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a914996508a498faac0d74e21536cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4f8b2dcaf2be0c42f852400d758acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
4 . (1)在
的展开式中,求形如
(
,
)的所有项的系数之和.
(2)证明:
展开式中的常数项为
.
(3)设
的小数部分为
,比较
与1的大小
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a94cee4761bbe64fbeabd6011a07ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c908a876be601f54c1af6cf77a445685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9a9067fce21d7f9e6108766dd7067a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ab55bbc2761abe6b82ccf9456881b4.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487aaa5d6a92b34f9019a6531258d17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb1855504bc8be2becec8d259e7f199.png)
您最近一年使用:0次
7日内更新
|
156次组卷
|
3卷引用:山东省聊城第三中学等校2023-2024学年高二下学期5月质量监测联合调考数学试题
名校
解题方法
5 . 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)
您最近一年使用:0次
7日内更新
|
576次组卷
|
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
6 . 第19届亚运会于2023年9月23日至10月8日在杭州举行,为弘扬奥林匹克和亚运精神,增强锻炼身体意识,某学校举办一场羽毛球比赛.已知羽毛球比赛的单打规则是:若发球方胜,则发球方得1分,且继续在下一回合发球;若接球方胜,则接球方得1分,且成为下一回合发球方.现甲、乙二人进行羽毛球单打比赛,根据以往甲、乙两名运动员对阵的比赛数据可知,若甲发球,甲得分的概率为
,乙得分的概率为
;若乙发球,乙得分的概率为
,甲得分的概率为
.规定第1回合是甲先发球.
(1)求第3回合由甲发球的概率;
(2)①设第i回合是甲发球的概率为
,证明:
是等比数列;
②已知:若随机变量
服从两点分布,且
,
,2,…,n,则
.若第1回合是甲先发球,求甲、乙连续进行n个回合比赛后,甲的总得分的期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
(1)求第3回合由甲发球的概率;
(2)①设第i回合是甲发球的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5c607987b73502db63f77c9799f4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bfab5f9cb89603b6313c971285ff3b.png)
②已知:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ef015dfcb4e200426d5f54ba6deec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece16154c3be9e43a5dd37a91d7d8c3b.png)
您最近一年使用:0次
解题方法
7 . 为了解学生中午的用餐方式(在食堂就餐或点外卖)与最近食堂间的距离的关系,某大学于某日中午随机调查了2000名学生,获得了下面的频率分布表(不完整),并且由该频率分布表,可估计学生与最近食堂间的平均距离为
(同一组数据以该组数据所在区间的中点值作为代表).
(1)求出
的值并补全频率分布表;
(2)根据频率分布表补全样本容量为
的
列联表(如下表),并根据小概率值
的独立性检验,能否认为学生中午的用餐方式与学生距最近食堂的远近有关(当学生与最近食堂间的距离不超过
时,认为较近,否则认为较远);
根据频率分布表列出如下的
列联表:
(3)一般情况下,学生更愿意去饭菜更美味的食堂就餐.该校距李明较近的有甲、乙两家食堂,且他每天中午都选择食堂甲或乙就餐.记他选择去甲食堂就餐为事件A,他认为甲食堂的饭菜比乙食堂的美味为事件D,且D、A均为随机事件,证明:
.
附:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc799084b142019f173728370a7bc32e.png)
学生与最近食堂间的距离![]() | ![]() | ![]() | ![]() | ![]() | ![]() | 合计 |
在食堂就餐 | 0.15 | 0.10 | 0.00 | 0.50 | ||
点外卖 | 0.20 | 0.00 | 0.50 | |||
合计 | 0.20 | 0.15 | 0.00 | 1.00 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)根据频率分布表补全样本容量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abb59695562b3a1295a251dc97da700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ba29eb90358e2211e1f7ba6423fa2.png)
根据频率分布表列出如下的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
学生距最近食堂较近 | 学生距最近食堂较远 | 合计 | |
在食堂就餐 | |||
点外卖 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169d6162056f4486756c34256f5a4cd7.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![]() | 0.10 | 0.010 | 0.001 |
![]() | 2.706 | 6.635 | 10.828 |
您最近一年使用:0次
8 . 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)
您最近一年使用:0次
名校
解题方法
9 . 在一条只能沿单向行驶的高速公路上,共有
个服务区.现有一辆车从第
个服务区向第1个服务区行驶,且当它从第
个服务区开出后,将等可能地停靠在第
个服务区,直到它抵达第1个服务区为止,记随机变量
为这辆车全程一共进入的服务区总数.
(1)求
的分布列及期望;
(2)证明:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f27f84764f1cca89ce3d93fc1cf603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dbd3cfdfc5434d53191175f7f658ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56f2ed1c214ad049f0af70377585962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bbb0a939ec3c2d0414c2351f93ae5f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570b23a0c53f8a2e896900acb8f21c03.png)
您最近一年使用:0次
2024-06-03更新
|
905次组卷
|
2卷引用:山东省日照市五莲县第一中学2024届高三第三次模拟考试数学试题
解题方法
10 . 我国古代数学家赵爽为了证明勾股定理,创制了一副“弦图”.后人称其为“赵爽弦图”.如图,现提供5种颜色给图中的5个小区域涂色,规定每个区域只涂一种颜色,相邻区域颜色不相同.记事件
:“区域2和区域4颜色不同”,事件
:“所有区域颜色均不相同”,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f2666380ef520111b6a1484f56372f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次