已知正項(xiàng)等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905372481.png)
滿足:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905388593.png)
,若存在兩項(xiàng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905388479.png)
使得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905419641.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905466580.png)
的最小值為
;
試題分析:因?yàn)閿?shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905372481.png)
為正項(xiàng)等比數(shù)列,設(shè)公比為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905497310.png)
, 則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905544603.png)
解得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905560432.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905575415.png)
(舍)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905591889.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905606609.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031905622537.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319056381288.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319056531192.png)
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