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1 . 已知递增等比数列
满足
,则
的前三项依次是__________ .(填出满足条件的一组即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce1db8ea6ca42113d45217ab4133f34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
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2019-04-08更新
|
539次组卷
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6卷引用:2019届重庆市南开中学高三下学期月考数学理科试题
2019届重庆市南开中学高三下学期月考数学理科试题【市级联考】云南省昆明市2019届高三复习教学质量检测理科数学试题(已下线)第一章 数列(能力提升)-2020-2021学年高二数学单元测试定心卷(北师大版必修5)辽宁省葫芦岛市2021-2022学年高二下学期期末数学试题【市级联考】云南省昆明市2019届高三复习教学质量检测文科数学试题(已下线)模块四 专题2 期末重组综合练(辽宁)(高二人教B)
2 . 进位制是人们为了计数和计算方便而约定的记数方式,通常“满二进一,就是二进制;满八进一,就是八进制;满十进一,就是十进制……;满几进一,就是几进制”.
我们研究的正整数通常是十进制的数,因此,将正整数
的各位上的数字分别记为
,则
表示为关于10的
次多项式,即
,其中
,
,记为
,简记为
.
随着计算机的蓬勃发展,表示整数除了运用十进制外,还常常运用二进制、八进制等等.更一般地,我们可类似给出
进制数定义.
进制数的定义:给出一个正整数
,可将任意一个正整数
,其各位上的数字分别记为
,则
唯一表示为下列形式:
,其中
,
,并简记为
.
进而,给出一个正整数
,可将小数
表示为下列形式:
,其中
,
,并简记为
.
(1)设
在三进制数下可以表示为
,
在十进制数下可以表示为
,试分别将
转化成十进制数,
转化成二进制数;
(2)已知数列
的前
项和为
,且满足
,
,数列
满足,当
时,
;
①当
时,求数列
的通项公式;
②证明:当
时,
.
我们研究的正整数通常是十进制的数,因此,将正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23dd0a10a73674c8a47420d7e91da0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432851e0d0b7a2924da29b9cc5ca1706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c95c671f517c02f1deccd2174f7465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f856d17cdd7499eeea956845fe51ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ceec6993cc9e39a5d5e6097d6447c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d5a7b02c9d7bd9e2910849ab591fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856f717993779ce676195ed3c8074e15.png)
随着计算机的蓬勃发展,表示整数除了运用十进制外,还常常运用二进制、八进制等等.更一般地,我们可类似给出
![](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/50e3273deabbf8c7d700d340b71ca2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c89fe2197a7044536c5c3b52789636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f285903ef04eb7a1d2071cb7197521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22a19eeff39dff098ea766cf74d3c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d2aae1ce527125960613e78e1bb501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2a4ce3547aff6aebdd145d11c566fe.png)
进而,给出一个正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e3273deabbf8c7d700d340b71ca2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20277d6743703a3710d6ceb8dc869cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ef1766237596595c550af4600c370e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e6d4140fcd9583fe03f91701ae083f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74304131e01d0e9e68bd8a566b30d529.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dc317d03cfed7687fad0448c298f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d9abc918557b3bd56cb30dfd20b91f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/fb451756eab7b736e0c576e03f6243b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931b93e6ee1145e185621ae08dbf170f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26663935b7cb86ca81ad2aa73d49e26a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931b93e6ee1145e185621ae08dbf170f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
②证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931b93e6ee1145e185621ae08dbf170f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac363332016ae0fa59a5e4a1d41e2a0b.png)
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3 . 一个质点在一条直线上“随机游走”,向左走一步和向右走一步的概率均为
,试探讨下列问题:
(1)若质点进行了4次“随机游走”,在其中恰有2次向右游走的情况下,求第二次向左游走的概率;
(2)记
为
次游走中恰有2次向右游走的概率,令
.记
为不超过
次游走的情况下,向右游走2次后停止游走(若向右游走一直不足2次,在游走到
次时也停止游走),此时一共游走的次数,
的数学期望为
.请比较
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)若质点进行了4次“随机游走”,在其中恰有2次向右游走的情况下,求第二次向左游走的概率;
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdffb332396f83e73c674cc52e62d94e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5110f3ef4b6b1c5446ef0d4aad744ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c947bebcce27a67b2793e93e7fd91809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573705072a4ea0f7ccfaf61dcaab8d34.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/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a123f4954cc3e526fd05619f64616b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a123f4954cc3e526fd05619f64616b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2248664f78c5b4b85c4400574da7d3.png)
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