解题方法
1 . 入冬以来,东北成为全国旅游和网络话题的“顶流”.南方的小土豆们纷纷北上体验东北最美的冬天,这个冬天火的不只是东北的美食、东北人的热情,还有东北的洗浴中心,拥挤程度堪比春运,南方游客直接拉着行李箱进入.东北某城市洗浴中心花式宠“且”,为给顾客更好的体验,推出了
和
两个套餐服务,顾客可自由选择
和
两个套餐之一,并在App平台上推出了优惠券活动,下表是该洗浴中心在App平台10天销售优惠券情况.
经计算可得:
,
,
.
(1)因为优惠券购买火爆,App平台在第10天时系统出现异常,导致当天顾客购买优惠券数量大幅减少,现剔除第10天数据,求
关于
的经验回归方程(结果中的数值用分数表示);
(2)若购买优惠券的顾客选择
套餐的概率为
,选择
套餐的概率为
,并且
套餐可以用一张优惠券,
套餐可以用两张优惠券,记App平台累计销售优惠券为
张的概率为
,求
;
(3)记(2)中所得概率
的值构成数列
.
①求
的最值;
②数列收敛的定义:已知数列
,若对于任意给定的正数
,总存在正整数
,使得当
时,
,(
是一个确定的实数),则称数列
收敛于
.根据数列收敛的定义证明数列
收敛.
参考公式:
,
.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
日期![]() | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
销售量![]() | 1.9 | 1.98 | 2.2 | 2.36 | 2.43 | 2.59 | 2.68 | 2.76 | 2.7 | 0.4 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/decf6657efa807fc90353c5e6be0a263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0064de1b957bc9b668565180e34f6f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f36001b6081f8168466384adb24065c.png)
(1)因为优惠券购买火爆,App平台在第10天时系统出现异常,导致当天顾客购买优惠券数量大幅减少,现剔除第10天数据,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若购买优惠券的顾客选择
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(3)记(2)中所得概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd7841ef44b17863697517fb5f3039d.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
②数列收敛的定义:已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711c92626a97e6b778b3aa86e663ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512e8bacfff15253901cd216a1e42013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5a325806df1a1c3e7ce609fe99085f.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa225ad36ee50c40869d87f694b6c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
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2024-05-07更新
|
1677次组卷
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3卷引用:东北三省四城市联考暨沈阳市2024届高三下学期数学质量检测(二)
解题方法
2 . 已知数列
的通项公式为
,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/196c5dceb4207bcb38bdd1a1b6a5d62b.png)
A.若![]() ![]() |
B.若对任意![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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