题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045250-43327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045250-37389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045250-20424.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045250-23555.gif)
⑴求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045251-58608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045250-43327.gif)
⑶求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045251-61629.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045251-72360.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045251-65103.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045252-50377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045252-60577.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045252-21707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045252-66743.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045251-58608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045251-72360.gif)
⑵由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045252-61711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045253-33555.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045253-42004.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045251-65103.gif)
⑶∵
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045253-39060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045253-98964.gif)
(或由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045253-33677.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045254-10353.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045250-43327.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045254-60528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045254-41493.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045254-57501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045254-72611.gif)
核心考点
举一反三
a21,a22,……a28
……………………
64个正数排成8行8列, 如下所示: a81,a82,……a88
在符合
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045236-46076.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045236-76598.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045237-95911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045237-92692.gif)
⑴若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045237-91596.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045237-47631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045237-29251.gif)
⑵记第n行各项之和为An(1≤n≤8),数列{an}、{bn}、{cn}满足
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045238-24530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045238-63212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045238-75783.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045238-23160.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045238-86805.gif)
⑶对⑵中的
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045239-86011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045239-44007.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045239-66383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045239-47096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045220-57621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045221-82818.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045221-67838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045221-97220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045221-79539.gif)
求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045220-57621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045221-41559.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045222-89614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045222-58892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045221-67838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045222-84344.gif)
(1)证明数列{an-n}是等比数列;(2)求数列{an}的前n项和Sn;(3)证明不等式Sn+1≤4Sn,对任意n∈N*皆成立。
1 -----------第一行
2 2 -----------第二行
3 4 3 -----------第三行
4 7 7 4 -----------第四行
5 11 14 11 5
… … … …
… … … … …
假设第
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045155-27013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045155-98778.gif)
(Ⅰ)依次写出第六行的所有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045155-49252.gif)
(Ⅱ)归纳出
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045155-96444.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045155-35327.gif)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045156-35947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045156-65848.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045156-89587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045122-40091.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045123-97787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045123-24564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045123-10966.gif)
(1)求a
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045123-94184.gif)
(2)试归纳出第n行中第m个数a
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045123-56802.gif)
(3)记S
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045124-79481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045124-34334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045124-11108.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045124-60092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045124-60644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045125-98557.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013045125-20883.gif)
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