题目内容
已知数列
满足![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158574641109.png)
(1) 求![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857636169.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857651348.png)
(2) 求数列
的前
项和![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857714388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857417480.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158574641109.png)
(1) 求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857636169.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857651348.png)
(2) 求数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857667550.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857683297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857714388.png)
(1)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857745956.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857729637.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857745956.png)
(1)本小题是由前n项和求通项的问题类型.一般做法是n=1,
;
当
时,
,然后验证n=1时,是否满足上式,不满足写成分段函数的形式.满足写成一个式子即可.
(2)根据(1)可知
显然易采用错位相减的方法求解
(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857870235.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158580411112.png)
当
时,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158582291184.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858275947.png)
当
满足![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858322667.png)
综上:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858322667.png)
(2)、![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857839724.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158584311210.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158584471206.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158584632068.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858478975.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857776448.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857792435.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857823564.png)
(2)根据(1)可知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857839724.png)
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857870235.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158580411112.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858057437.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158582291184.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858260674.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858275947.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858307635.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858322667.png)
综上:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858322667.png)
(2)、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215857839724.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158584311210.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158584471206.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232158584632068.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215858478975.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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