已知数列
满足
,
,
,
.
(1)求证:数列
是等比数列;
(2)记数列
的前
项和为
,数列
的前
项和为
,是否存在常数
,使得
,若存在,求出
的值;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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32aa4bb7dbc79e76acf0e3f33d0c0d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a89e23cbb54c644241cd0231c09bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记数列
![](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/034ba25825c13725931c483aa47c9363.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/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afaea3b51f27b0499cccdca51cf01fd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
23-24高三上·重庆沙坪坝·期中 查看更多[3]
重庆市沙坪坝区南开中学校2024届高三上学期第四次质量检测(期中)数学试题(已下线)模块一专题2《数列的通项公式与求和》单元检测篇B提升卷(高二人教B版)(已下线)模块一 专题3《数列的通项公式与求和》单元检测篇B提升卷(高二北师大版)
更新时间:2023-12-02 11:44:58
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【推荐1】某人在工作一段时间后制定了如下理财计划:将自己第一年末的总资产均分成两半,一半进行再投资,获取资金增值,另一半留在身边作为备用金,并支付生活费开支,第二年末将当年固定收入,投资的本金和收益与身边备用金的余额合并,并按加上理财计划进行再分配,以此类推,已知投资部分每年获得4%的收益,生活费开支需要每年
万元.
(1)若此人每一年末总资产
为
万元,每年有固定收入
万元,到第
年末,此人的总资产为
,试证明数列
为等比数列,并求
的通项公式;
(2)若此人
岁退休时有总资产
万元,此后每年固定收入为
元,按照他的理财计划,那么在他第几岁那一年内,将会遇到个人财政赤字(即当年的备用金低于当年的生活费开支)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
(1)若此人每一年末总资产
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96eb217f9243c3ca00e78d85da125834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若此人
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3779b4ea5477aebfe85113b0de1d60.png)
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解题方法
【推荐2】已知单调递增的等比数列
满足
,且
是
,
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(2)若数列
满足
,求数列
的通项公式;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3692d1cd54aaa7e2321fff5142e5d2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d473bfcc52ebc119430335531488a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4432f827eacbf57677627bfcffc81140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
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【推荐1】已知函数
,
,满足:①对任意
,都有
;②对任意
都有
.
(1)试证明:
为
上的单调增函数;
(2)求
;
(3)令
,
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e205a7dc01a9e0bd2a8cb8bb1cc8ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7580d0a4f97c273f20e95b0fe566e705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958c91e0cc2cf4f17acb778de21846b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c199c596534dd80309fc1caf4c96b2.png)
(1)试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891d3c5fdf4d8eb207202a0d14e076cb.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79a776eb388794b659f7c2d6498eb09.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5878e2bf9d209e149fcccbbb11c4bcbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0071819dbd79ab39691eb051d909ddae.png)
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【推荐2】已知数列
满足:
=1,
.
(1)求证:数列
是等比数列;
(2)设
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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(1)求证:数列
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(2)设
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【推荐1】已知公差不为0的等差数列
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(1)求数列
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(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
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【推荐2】已知等比数列
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是数列
的前
项积,请求出
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的值.
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求数列
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(2)若
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【推荐1】已知等比数列
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,
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(2)设
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.
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(2)设
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【推荐2】已知等差数列
满足:
,
.
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbfd6b761451716ba3d7130c93497ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e707ece9ff208755f8ce6852827d73aa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11f62d9718cbadfe12826fe9607ff97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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