题目内容
数列
的通项公式
,则该数列的前( )项之和等于9。
( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752248494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752451726.png)
( )
A.98 | B.99 | C.96 | D.97 |
B
分析:先将分母有理化,再利用叠加法可求和,进而可得结论
解答:解:∵
,
∴an=
-
,
∴Sn=
-1+
-
+…+
-![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752591292.png)
=
-1=9
∴
=10,
∴n=99
故选B.
解答:解:∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752451726.png)
∴an=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752576362.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752591292.png)
∴Sn=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752622344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752638344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752622344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752576362.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752591292.png)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752576362.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823185752576362.png)
∴n=99
故选B.
![](http://thumb2018.1010pic.com/images/loading.gif)
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A.98 | B.99 | C.96 | D.97 |