题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-74119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-54109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-35836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-28150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-34499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-50057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-42237.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-74119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-28150.png)
(2) 记
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-52121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-36029.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-71326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-21974.png)
(2)利用数列的单调性,结合定义法作差法来得到单调性的证明。
解析
试题分析:解:(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-54109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055255-35836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-35744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-63103.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055258-72080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055258-97241.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-71326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-42237.png)
又当n=1时,有b1=S1=1-
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055258-90659.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055258-90557.png)
∴数列{bn}是等比数列,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055258-56246.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055257-21974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055256-42237.png)
(Ⅱ)由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055309-18127.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055310-26658.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055310-17650.png)
点评:解决的关键是能利用等差数列的概念和等比数列的通项公式来求解,属于基础题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-87837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-18783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-32332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-14453.png)
(1)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-32332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-93537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-82736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-19197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055235-98923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055236-68545.png)
(2)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-32332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055234-18783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-26199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-21277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-83758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-66453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-26199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055214-98105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055215-14784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055215-72867.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055207-29511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055207-97750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055207-34416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055208-38449.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055151-20401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055151-42943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055152-69768.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055145-78408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055145-27820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055145-70082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055145-23450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055145-60244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012055146-37090.png)
A.17 | B.18 | C.19 | D.20 |
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