题目
题型:不详难度:来源:
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050509-27941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050509-49421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050509-61224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050510-88934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050510-73788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050510-51135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050510-47271.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050509-27941.png)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050510-88934.png)
(Ⅲ)证明:对于
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050510-46614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050511-54597.png)
答案
所以 2Sn+1=(n+2)an+1.
两式相减得 2an+1=(n+2)an+1-(n+1)an,即
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050511-39636.png)
当n≥2时,
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050511-43537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050511-46417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050512-69688.png)
又a1=2满足上式,故
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050511-43537.png)
(Ⅱ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050512-91559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050512-39957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050512-38399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-91783.png)
故当n≥3时,有
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-96013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-91783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-66115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-15892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-66115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-17522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-66115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050514-15304.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-96013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050514-31354.png)
显然 b
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050512-38399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-91783.png)
故 {
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-96013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050513-96013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050514-31354.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050514-10112.png)
当k≥2时,
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050514-92162.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050514-70437.png)
注意到 b1=0,
则
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050515-38372.png)
解析
核心考点
试题【(本小题满分12分)已知数列的前n项和为 (n∈N*),且.数列满足,,,n=2,3,….(Ⅰ)求数列 的通项公式;(Ⅱ)求数列 的通项公式;(Ⅲ)证明:对】;主要考察你对数列综合等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050458-17807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050458-95836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050459-18442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050459-74483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050459-49270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050459-44861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050500-51178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050500-25197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050500-64615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050500-46978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050501-62051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050501-69661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050454-91637.png)
(1)求a1和a2的值;
(2)求数列{an},{bn}的通项an和bn;
(3)设cn=an·bn,求数列{cn}的前n项和Tn.
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050450-51282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050450-11063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050450-84230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050437-93871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050437-51923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050437-83833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050437-64325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050437-83833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050438-83929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050438-60342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050438-85456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050438-50032.png)
⑴求
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050439-23984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050439-44006.png)
⑵求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050439-61801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050440-13782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050440-83038.png)
⑶ 设
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050440-49040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050440-71297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050441-30350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015050427-27999.png)
A.190 | B.171 | C.90 | D.45 |
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