题目内容
(本小题满分12分)
已知等差数列
中,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420141798.png)
为数列
的前
项和.
(1)求数列
的通项公式;
(2) 若数列
的公差为正数,数列
满足
, 求数列
的前
项和![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420344373.png)
已知等差数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420125481.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420141798.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420172388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420125481.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420203297.png)
(1)求数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420125481.png)
(2) 若数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420125481.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420250491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420266585.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420250491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420203297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420344373.png)
(1)设
的公差为
,则![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114203901234.png)
即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114204061150.png)
解得
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420437733.png)
因此
或
………….6分
(2)当公差为正数时,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420500936.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114205151514.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114205312062.png)
……………………….12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420125481.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420375321.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114203901234.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114204061150.png)
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420422744.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420437733.png)
因此
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420468853.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420484964.png)
(2)当公差为正数时,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420500936.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114205151514.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114205312062.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114205461755.png)
(1) 由已知
根据通项公式求
,(2) 求出
,利用裂项相消法求和。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420141798.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420422744.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211420266585.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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