题目内容
(本小题满分15分)
设等差数列
的前
项和为
,等比数列
的前
项和为
已知数列
的公比为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442622787.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442763840.png)
(1)求数列
,
的通项公式;
(2)求![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442825963.png)
设等差数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442451481.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442466297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442482388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442497487.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442466297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442529397.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442497487.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442622787.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442763840.png)
(1)求数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442451481.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442497487.png)
(2)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442825963.png)
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442903527.png)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442919562.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442887603.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442903527.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442919562.png)
(1)利用等差和等比数列的定义和性质列出关于数列的参数,进一步求出数列的通项公式;(2)根据数列通项选择裂项求和思想求出数列的前n项和
解:(1)设
的公差为
,则
.解得
,所以
.
由
,得
,又
,从而解得
,所以
.
(2)
.
所以
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232154435741337.png)
=
=
=
.
解:(1)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442934480.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443168321.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443184744.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443215408.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442887603.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443262579.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443293609.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443309423.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443371408.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442903527.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232154434021473.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232154434181150.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232154435741337.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443589914.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215443605887.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215442919562.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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