题目内容
(本小题满分12分)
如图5,已知曲线
。从C上的点Qn(
)作x轴的垂线,交
于点
,再从
作y轴的垂线,交C于点
。设![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731433665.gif)
(I)求
的值,由此猜想数列
的通项公式(不用证明);
(II)设
和面积为
,求证![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731589399.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731651944.gif)
如图5,已知曲线
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731074855.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731090357.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731121224.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731152218.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731152218.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731386520.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731433665.gif)
(I)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731449392.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731464267.gif)
(II)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731480639.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731495676.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731589399.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731651944.gif)
(I)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731683592.gif)
(II)证明见解析。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731683592.gif)
(II)证明见解析。
(I)由题意知![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731698661.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231427317141546.gif)
…………2分
猜想
…………4分
(II)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731761861.gif)
…………8分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231427317921702.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731807665.gif)
,
…………10分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731854821.gif)
…………12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731698661.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231427317141546.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731729684.gif)
猜想
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731683592.gif)
(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731761861.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231427317761094.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231427317921702.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731807665.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731823619.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731839568.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142731854821.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231427318701619.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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