等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900684457.png)
中,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900700665.png)
,若數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900715613.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900731297.png)
項(xiàng)和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900762432.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900731297.png)
的值為
。
試題分析:因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900700665.png" style="vertical-align:middle;" />,所以公差
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900887714.png)
,所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240019009181110.png)
,
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240019009341047.png)
,所以數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900715613.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001900731297.png)
項(xiàng)和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240019011834114.png)
,所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001901199425.png)
。
點(diǎn)評:常見的裂項(xiàng)公式:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001901215745.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001901230983.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240019012611134.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240019012771396.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001901293801.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240019013241074.png)
。
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