在數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054922953466.png)
中,若對任意的
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054922968503.png)
均有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054922999513.png)
為定值,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054923015681.png)
,則數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054922953466.png)
的前100項(xiàng)的和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054923062379.png)
( )
試題分析:根據(jù)已知:對任意的
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054922968503.png)
均有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054922999513.png)
為定值,
可知該數(shù)列從首項(xiàng)起,三項(xiàng)一循環(huán).即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054923124754.png)
;
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054923140772.png)
;
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054923155721.png)
,
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240549231711547.png)
.
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