题目内容
求下列数列的一个通项公式:
⑴![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111606389.gif)
⑵![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111622577.gif)
⑶![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111638819.gif)
⑷![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111653554.gif)
⑴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111606389.gif)
⑵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111622577.gif)
⑶
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111638819.gif)
⑷
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111653554.gif)
⑴
⑵
⑶
⑷![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111731545.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111669421.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111684574.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111700699.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111731545.gif)
⑴联想数列
即数列
,可得数列的通项公式
;
⑵将原数列改写为
分母分别为
分子分别为
呈周期性变化,可以用
,或
,或
表示.
(或
,或
)
⑶分子为正偶数列,分母为
得 ![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111700699.gif)
⑷观察数列可知:![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123112012840.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231231120281491.gif)
本题也可以利用关系式
求解.
【名师指引】⑴联想和转换是由已知认识未知的两种有效的思维方法.
⑵求数列的通项公式,应运用观察、分析、归纳、验证的方法.易错之处在于每个数列由前几项找规律不准确,以及观察、分析、归纳、验证这四个环节做的不够多,应注意对每一数列认真找出规律和验证.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111747517.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111762388.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111669421.gif)
⑵将原数列改写为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111809835.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111840334.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111856329.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111872444.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111887541.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111903476.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111684574.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111934612.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111965573.gif)
⑶分子为正偶数列,分母为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111981674.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123111700699.gif)
⑷观察数列可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123112012840.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231231120281491.gif)
本题也可以利用关系式
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123112184422.gif)
【名师指引】⑴联想和转换是由已知认识未知的两种有效的思维方法.
⑵求数列的通项公式,应运用观察、分析、归纳、验证的方法.易错之处在于每个数列由前几项找规律不准确,以及观察、分析、归纳、验证这四个环节做的不够多,应注意对每一数列认真找出规律和验证.
![](http://thumb2018.1010pic.com/images/loading.gif)
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