题目内容
观察下列各式:(x-1)(x+1)=x
–1
(x-1)(x
+x+1)=x
-1
(x-1)(x
+x
+x+1)=x
-1
(x-1)(x
+x
+x
+x+1)=x
-1
(1) 根据前面各式的规律可得:(x-1)(x
+x
+…+x+1)= 、(其中n为正整数)
(2)根据(1)求:1+2+2
+2
+…+2
+2
的值,并求出它的个位数字。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020684242.png)
(x-1)(x
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020684242.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020715242.png)
(x-1)(x
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020715242.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020684242.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020762220.png)
(x-1)(x
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020762220.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020715242.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020684242.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020824240.png)
(1) 根据前面各式的规律可得:(x-1)(x
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020840238.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020855292.png)
(2)根据(1)求:1+2+2
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020684242.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020715242.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020902284.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020918298.png)
①
②原式=
=
∴
的个位数字是5
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020949446.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020964966.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020980427.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823022020980427.png)
①观察其右边的结果:第一个是x2-1;第二个是x3-1;…依此类推,则第n个的结果即可求得.
②根据①求解
②根据①求解
![](http://thumb.zyjl.cn/images/loading.gif)
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