题目
题型:不详难度:来源:
![](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)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-22529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-21935.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-16127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-65638.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-32748.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-22529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-21935.png)
第二问中,∵
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-63413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-94100.png)
∴数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-28826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-16127.png)
第三问中,
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143700-44955.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143700-27015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143701-24300.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143701-60735.png)
由条件可知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143701-73210.png)
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143701-82102.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-22529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-21935.png)
(2)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-63413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-94100.png)
∴数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-28826.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143702-46371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-16127.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143700-44955.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143700-27015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143701-24300.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143701-60735.png)
由条件可知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143701-73210.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143702-10641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143702-57701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143702-63789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143702-57701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143703-86646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143703-86646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143703-99011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143703-41082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143703-48730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143704-30885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143704-41438.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143704-11638.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143704-56060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143703-99011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143704-38560.png)
综上知:实数
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143648-96502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010143649-65638.png)
核心考点
举一反三
![](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)
已知数列{an}满足a1=
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010142517-57591.png)
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