题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143721-32241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143721-25985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143721-93396.png)
1)写出数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-13727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-85577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143721-93396.png)
2)求经过多少年后,该项目的资金可以达到或超过
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-23990.png)
答案
解:1)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-69332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-41719.png)
猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-50835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-88573.png)
2)要经过
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-42981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-23990.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-69332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-41719.png)
猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-50835.png)
第二问中,由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-86572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-16917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-58299.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-24286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-24368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-44933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143725-77233.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143725-82554.png)
解:1)依题意
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-69332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-41719.png)
猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-50835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-88573.png)
2)由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-86572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-16917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-58299.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-24286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-24368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143724-44933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143725-77233.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143725-82554.png)
答:要经过
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143723-42981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143722-23990.png)
核心考点
试题【某企业投资1千万元于一个高科技项目,每年可获利25%.由于企业间竞争激烈,每年底需要从利润中取出资金万元进行科研、技术改造与广告投入,方能保持原有的利润增长率.】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143646-10356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143646-62908.png)
1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143646-35174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143647-97121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143647-59697.png)
3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143647-85007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143647-16542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-96502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143635-18684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143636-79372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143636-80462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143636-13871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143636-26320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143636-25139.png)
已知数列{an}满足Sn+an=2n+1,
(1) 写出a1, a2, a3,并推测an的表达式;
(2) 用数学归纳法证明所得的结论。
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142924-83222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142925-87849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142925-78278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142925-19809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142925-42076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142926-31264.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142924-83222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142925-42076.png)
(Ⅱ)是否存在
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142926-59553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142926-87160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142925-42076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142926-31985.png)
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142535-85141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142535-48002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142536-35258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142536-51659.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142536-57004.png)
(2)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142536-17558.png)
(3)抽去数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142535-85141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142536-89011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142537-26096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142537-26096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142537-15467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142537-42775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142537-64828.png)
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