1 . 11分制乒乓球比赛,每赢一球得1分,当某局打成
平后,每球交换发球权,先多得2分的一方获胜,该局比赛结束.甲、乙两位同学进行单打比赛,假设甲发球时甲得分的概率为
,乙发球时甲得分的概率为
,各球的比赛结果相互独立.在某局比赛双方打成
平后,甲先发球.
(1)求再打2球该局比赛结束的概率;
(2)两人又打了
个球该局比赛结束,求
的数学期望
;
(3)若将规则改为“打成
平后,每球交换发球权,先连得两分者获胜”,求该局比赛甲获胜的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3c3ffbae2f4ed36909dca6aecbad18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3c3ffbae2f4ed36909dca6aecbad18.png)
(1)求再打2球该局比赛结束的概率;
(2)两人又打了
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(3)若将规则改为“打成
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3c3ffbae2f4ed36909dca6aecbad18.png)
您最近一年使用:0次
解题方法
2 . 已知数列
是斐波那契数列,其数值为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
.这一数列以如下递推的方法定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
.数列
对于确定的正整数
,若存在正整数
使得
成立,则称数列
为“
阶可分拆数列”.
(1)已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
.判断是否对
,总存在确定的正整数
,使得数列
为“
阶可分拆数列”,并说明理由.
(2)设数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
,
(i)若数列
为“
阶可分拆数列”,求出符合条件的实数
的值;
(ii)在(i)问的前提下,若数列
满足
,
,其前
项和为
.证明:当
且
时,
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc50612eece655796b752da6b4bc3f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d74fa7fa6330976d7eb8e523a62cd09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cdfd9c3f8933cddb63d87dbe2812994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753358ca020523f27725f5187bb8e988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136a003907c455bfd58875c96c138772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79282bbe9f6408297d6378878c423bec.png)
(i)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)在(i)问的前提下,若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5f894d605847c6df0c4df24cf8e1fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a340cb0e3c456ec64ffdf89d7cd6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48268fd6d3f92032eb54fbf65c01405.png)
您最近一年使用:0次
解题方法
3 . 设数列
满足
,且
.
(1)求
的通项公式;
(2)求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eefa3d07b96cd30478c53b288e248e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](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)
您最近一年使用:0次
名校
解题方法
4 . 根据统计数据,某种植物感染病毒之后,其存活日数X满足:对于任意的
,
的样本在
的样本里的数量占比与
的样本在全体样本中的数量占比相同,均等于
,即
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4111fbeeb20975034f051295bc7bb1f2.png)
__________ ,设
,
的前n项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05d83daef7bb72f157ed504d3a1708c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bbadf6bea687b3de5dd1afe160a020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ce9db5574a2df6184bdc7cd13b208a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc7e207019873e3b048a13d4876c952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4111fbeeb20975034f051295bc7bb1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea3df8f05aab080084fe846c692c321.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/04c2864e2ec3416cc4c081ac1f71a0af.png)
您最近一年使用:0次
2024-06-09更新
|
515次组卷
|
3卷引用:山东省临沂市2024届高三下学期5月高考模拟考试(二模)数学试题
5 . 已知数列
,数列
是等差数列.且满足
.
(1)求数列
和
的通项公式;
(2)若
,求数列
的前
项和
;
(3)设数列
的前
项和为
,若
且
,求集合A中所有元素的和S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e61eea630134461c03372d259534e9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e885b63770eceb375d9dd8120fbafb39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设数列
![](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/d2d541406cfd9b15bf7d88a2c2883f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a7878130ed7c092d3c9f5b7f534677.png)
您最近一年使用:0次
6 . 我们知道,在平面内取定单位正交基底建立坐标系后,任意一个平面向量,都可以用二元有序实数对
表示.平面向量又称为二维向量.一般地,n元有序实数组
称为n维向量,它是二维向量的推广.类似二维向量,对于n维向量,也可定义两个向量的数量积、向量的长度(模)等:设
,
,则
;
.已知向量
满足
,向量
满足
.
(1)求
的值;
(2)若
,其中
,当
且
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c2af42141367e6e9ff0296c31daa7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b3b354facacd72bc68da6ac07be453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48d974578eb15ca117e0cb1b59788d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99aa60676891adca75eac086182a15c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581496116ddfba6dd03722fd771d5a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5babafd9f4e5c3c222ba25a3de66794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48d974578eb15ca117e0cb1b59788d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cb2f5c0569962cd7c1026f388cb661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99aa60676891adca75eac086182a15c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4492fb816272cd60cf3456c6a064020e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa3e5481ce1f11ea4cb1d1ddc71413.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301fa5679316c282923735aff9285559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ac252e9126ab540c0102b941f0ee42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74cac554f22f3655ef6691b2ef821eac.png)
您最近一年使用:0次
名校
解题方法
7 . 数列
满足
,
,
,
表示
落在区间
的项数,其中
,则( )
![](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/99708a89389c873bdfb48e7a49902ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5745b57d8e86820da6790864dd3e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知等比数列
的前n项和为
,
,对任意
,
是
与
的等差中项.
(1)求
的公比q;
(2)求
的前n项和
.
![](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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0a9523f2084cf17b8656c11ab1d95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2422622b34b450e43d7e205f42428a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0620331265c321c19bc86f418a3e014d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daf61f4e47de374185652d6e0524938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
9 . 设
,y是不超过x的最大整数,且记
,当
时,
的位数记为
例如:
,
,
.
(1)当
时,记由函数
的图象,直线
,
以及x轴围成的平面图形的面积为
,求
,
及
;
(2)是否存在正数M,对
,
,若存在,请确定一个M的值,若不存在,请说明理由;
(3)当
,
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b7f26fe1977bda9de200debe99f020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888f3535e96d599e0840c74f44e90293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2fd68df194a8b9f184abb07ada0877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290d361e6c11b7c934a53d866a73522.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290e62b6c28d766f6a64fc6557667db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c9cfd43ce24a0d820f0044d9c837db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae72830ccc2633ada579cf63fd6932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831ed34d8c6d99fdd0b94688ef03bfcb.png)
(2)是否存在正数M,对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c21606ef2837d3a77d25e0c6473731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf968fe2653e0b497d78907096467d9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b95079ade5ac98fc651fafc489761f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49fd568e4f8120ace4d486adc764f55.png)
您最近一年使用:0次
解题方法
10 . 欧拉函数
的函数值等于所有不超过正整数
,且与
互质的正整数的个数,例如
.已知
,
,
是数列
的前
项和,若
恒成立,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b960464839ddd9760df08e0c73b80e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65867699d4d9e7361a39f2c6f7361041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e138f26d4d20f28121c1237ff5baa95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
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2024-05-15更新
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2卷引用:山东省烟台市2024年高考适应性练习(二模)数学试题