1 . 已知一数列
,满足递推条件
,
,求数列
的通项公式.
![](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/8b4f70d77792828e3307b786343ac7af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2 . 设数列
满足
,
.求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265b39d7ebedc37af64c2b7b22c37421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fba218f4823b4b2dd31f3634b8f0a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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3 . 数列
由
,
生成,讨论数列
的敛散性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069068a93772a4d02e4b3d2a6daa8fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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4 . 若设
,
,其中
为常数.试求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35b7e54ab699b6f8d52bce5f463976b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4cc00c283519973f7f8e1274b5c733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a460f28a8bf1bfe9d867828402bcccb.png)
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2023高三·全国·专题练习
5 . 数列
由
,
生成,讨论数列
的敛散性,若收敛,求出极限值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069068a93772a4d02e4b3d2a6daa8fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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6 . 如果
,
,1,2,…,其中a和q为常数,满足
,试证
收敛.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1c7cb189d4c4de9deb9715893c42f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca664b1e82da6f50064a76fe118aa80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
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2023高三·全国·专题练习
7 . 已知数列
满足:
,
,
(1)是否存在无穷数列
满足:对任意
有
?若存在,请求出
的取值范围;若不存在,请说明理由;
(2)若
,
是否存在?若存在,请求出该极限;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4f2833d643c792175027f0b524204b.png)
(1)是否存在无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882b660047bb6ded500cedba57958e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb3a970bf38d5616614fbc065edee88.png)
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8 . 记数列
的前
项和为
,若存在实数
,使得对任意的
,都有
,则称数列
为“和有界数列”. 下列命题正确的是( )
![](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/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1505d56f0b35fe7f2de1fe1888036e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b76b70a1c9c66d561996a2a3b389958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2023-05-24更新
|
892次组卷
|
5卷引用:第三篇 数列、排列与组合 专题6 有界变差数列 微点1 有界变差数列
(已下线)第三篇 数列、排列与组合 专题6 有界变差数列 微点1 有界变差数列(已下线)重难点突破01 数列的综合应用 (十三大题型)-1【全国百强校】浙江省嘉兴市第一中学2017-2018学年高一下学期期中考试数学试题河南省南阳市六校2021-2022学年高二上学期第一次联考数学(理)试题辽宁省沈阳市第一二〇中学2002-2023学年高二下学期期末数学试题
9 . 对于给定的正整数
,若数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe19f278fe87cde9d977ed0dc9febd0.png)
对任意正整数
总成立,则称数列
是“
数列”. 若数列
既是“
数列”,又是“
数列”,求证:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe19f278fe87cde9d977ed0dc9febd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c539dc67481e8b9ceaf3c7b83429d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ddb1294ab81b06f260fa8a40b7a1fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
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