题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113701-74089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113702-69981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113702-40186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113702-61858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113702-62880.png)
(I)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113703-48670.png)
(II)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113703-38148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113703-98496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113703-38148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113703-66727.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113704-79379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113704-37006.png)
解析
(1)因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113701-74089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113702-69981.png)
(2)由(1)知cn=12nan-n=6n×2n-n.,结合错位相减法得到和式
(I)由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113704-29349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113704-76483.png)
∴f (x)=2x-1,∴Sn=2n-1(n∈N*).……3分
∴当n≥2时,an=Sn-Sn-1=2n-2n-1=2n-1. ………4分
当n=1时, S1=a1=1符合上式. ………5分
∴an=2n-1(n∈N*). ………6分
(II)由(1)知cn=12nan-n=6n×2n-n. ………8分
从而Tn=6(1×2+2×22+…+n×2n)-(1+2+…+n)
错位相减法得:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113704-79379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113704-37006.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113528-40486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113528-50175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113528-32481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113529-80790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113528-32481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113050-89073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113050-66712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113050-97326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113050-41543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113051-66054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113001-82769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113001-15490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113001-29076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113002-17177.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113001-82769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113002-72061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113001-15490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113001-29076.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113002-95389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010113003-89358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010112956-31408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010112956-22087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010112957-77338.png)
A.2 | B.4 | C.8 | D.16 |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010112918-77458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010112918-66395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010112918-24201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010112918-80470.png)
A.13 | B.35 | C.49 | D.63 |
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