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解题方法
1 . 某公司一下属企业从事某种高科技产品的生产.该企业第一年年初有资金2000万元,将其投入生产,到当年年底资金增长了50%.预计以后每年年增长率与第一年的相同,公司要求企业从第一年开始,每年年底上缴资金
万元,并将剩余资金全部投入下一年生产.设第
年年底企业上缴资金后的剩余资金为
万元.
(1)用
表示
与
,并写出
与
的关系式;
(2)求证:当
时,数列
为等比数列,并说明
的现实意义;
(3)若公司希望经过
年使企业的剩余资金为4000万元,试确定企业每年上缴资金
的值.(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264c6a21014af96f07057f811e18715a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a9d12cae77e4674c8ad137adcccb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d55dbf1d85d5a0e3d9b68ffaa0aee74.png)
(3)若公司希望经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32242e0f13757d9272dbb9b2dde59396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-09-01更新
|
354次组卷
|
3卷引用:重庆市育才中学2021-2022学年高二上学期第五次定时练习数学试题
2010·全国·一模
2 . 已知数列
中,
,且点
在直线
上.
⑴求数列
的通项公式;
⑵若函数
(
,且
),求函数
的最小值;
⑶设
,
表示数列
的前
项和,试问:是否存在关于
的整式
,使得
对于一切不小于2的自然数
恒成立?若存在,写出
的解析式,并加以证明;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed98f3dfb393027271e6412db8399b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
⑴求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
⑵若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceb82fc725e0464bf20ee64ed771679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b3e1b506e10f0333dea0fb43eaab02.png)
⑶设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.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/cfd3ff88d9a2e571f91dc11fb9f80d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a6de0a55a4a5111be6089b13a0d930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd3ff88d9a2e571f91dc11fb9f80d6a.png)
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