题目内容
已知数列
的各项均为正数,前
项和为
,且![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158284171107.png)
(1)求证数列
是等差数列;
(2)设
…
,求
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828339480.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828355297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828386388.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158284171107.png)
(1)求证数列
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828339480.png)
(2)设
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828464958.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828495398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828511373.png)
(1)数列
是等差数列
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158285573453.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828542492.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158285573453.png)
(1)
,
当
时,![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158286671303.png)
当
时,由
(3’)
即
,
所以数列
是等差数列 (6’)
(2)由(1)可得
(8’)
(10’)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158288233462.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158285891160.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828620197.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828635366.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158286671303.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828682421.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158287131714.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158287291935.png)
所以数列
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828542492.png)
(2)由(1)可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215828776950.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158287911115.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232158288233462.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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