题目内容
数列
中,
.
⑴求数列
的最小项;
⑵判断数列
是否有界,并说明理由.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115553485.gif)
⑴求数列
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
⑵判断数列
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
⑴数列
的最小项为
⑵数列
有界
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115616297.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
⑴转化为判断数列的单调性,即证
,或
;⑵从“数列的有界性”定义入手.
⑴![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115678183.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115694875.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231231157091614.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115725128.gif)
,
数列
是递增数列,数列
的最小项为
.
⑵![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115678183.gif)
,
数列
有界.
【名师指引】数列是特殊的函数,判断函数的单调性、有界性的方法同样适用于数列.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115647392.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115662393.gif)
⑴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115678183.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115694875.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231231157091614.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115725128.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115647392.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115725128.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115616297.gif)
⑵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115678183.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115912896.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115725128.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123115506380.gif)
【名师指引】数列是特殊的函数,判断函数的单调性、有界性的方法同样适用于数列.
![](http://thumb2018.1010pic.com/images/loading.gif)
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