1 . 已知数列
满足
,
,
,则下列结论错误的是( )
![](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/12450dc3d97a4e15026ab56ae47bbd87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
A.![]() | B.存在![]() ![]() |
C.![]() | D.![]() |
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2 . 已知正项数列
满足
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdc4344f49b8da8bf84690885076ba7.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() |
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3 . 任取一个正整数,若是奇数,就将该数乘3再加上1;若是偶数,就将该数除以2.反复进行上述两种运算,经过有限次步骤后,必进入循环图
,这就是数学史上著名的“冰霓猜想”(又称“角谷猜想”等).已知数列
满足:
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a16f78ce0dab1ac8fa6abbd70f2b008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc73d432eb681f59489b833a7eab42e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2baa6c9a44e7c074327130d56084ba34.png)
A.1 | B.2 | C.3 | D.4 |
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4 . 已知正项数列
满足对任意正整数n,均有
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50bd4d63c6ce2d1f4b6fde323462463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172453ba1ada0276e7336b0d3cd09344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1082716588441c40b208fb80fa570c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-24更新
|
578次组卷
|
3卷引用:山东省淄博市实验中学2023-2024学年高二下学期第一次月考(3月)数学试卷
名校
5 . 任取一个正整数,若是奇数,就将该数乘3再加上1;若是偶数,就将该数除以2.反复进行上述两种运算,经过有限次步骤后,必进入循环图
,这就是数学史上著名的“冰霓猜想”(又称“角谷猜想”等).已知数列
满足:
,
则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a16f78ce0dab1ac8fa6abbd70f2b008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ed2fa976f3a906b4b1799b333d1d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acca5aa6b2285d897a65c289c1b54ba.png)
A.1 | B.2 | C.3 | D.4 |
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2024-02-14更新
|
319次组卷
|
4卷引用:山东省潍坊市临朐县第一中学2023-2024学年高二下学期3月月考数学试题
名校
解题方法
6 . 已知数列
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0adebbbc1fdb8dcce47722eb835917.png)
,
.
(1)证明:数列
是单调递增数列;
(2)记
,求
的取值范围;
(3)记
,试问
是否为定值?如果是,请证明,如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d12688460c5bedb198a6b5f06ef68c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0adebbbc1fdb8dcce47722eb835917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9dab85b367008f136f270f1eba0a7b.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3d05f1ea6d28a6b4728871e28fc9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7dcca2acb8fb6e6a6933a02e0a130b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c60d1623d5d89c47f988bbb1b21694.png)
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解题方法
7 . 若数列
满足
,
,则满足不等式
的最大正整数
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878591688b3edfd3c336365d416bff56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d540981311a78df02f06bcd11acc9a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.28 | B.29 | C.30 | D.31 |
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2024-01-11更新
|
646次组卷
|
6卷引用:山东省济南市莱芜第一中学2023-2024学年高二上学期第三次核心素养测试数学试题
山东省济南市莱芜第一中学2023-2024学年高二上学期第三次核心素养测试数学试题四川省内江市第三中学2024届高三上学期1月月考数学(理)试题(已下线)5.1.2 数列的递推(2知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)(已下线)第一章 数列(单元综合检测卷) -2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)河南省郑州市宇华实验学校2023-2024学年高二下学期4月期中考试数学试题四川省泸州市古蔺县蔺阳中学校2024届高三下学期二诊模拟考试理科数学试题
解题方法
8 . 已知函数
,若数列
满足
,
,
则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9d41144fc00b8fe94d2c863e7c85d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd5213f962d30402f2df6d81c8c61dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
A.该数列是周期数列且周期为3 | B.该数列不是周期数列 |
C.![]() | D.![]() |
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9 . 设
是数列
的前
项和,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/f2e20418c10bd073ecfd780d4d0b975c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
10 . 已知数列
满足
,设数列
的前n项和为
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107476767e4449eafab1762df9b9e126.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01421e274e88cdde68e461e7b36c90d8.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/11e2952ad592ce945553dc43465510ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cc7b68e217df5ab91284a2be6593c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107476767e4449eafab1762df9b9e126.png)
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