觀察下面的變形規(guī)律:
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162809280966.png)
=1﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162809314578.png)
;
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628096501047.png)
=
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162809690578.png)
﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162809731580.png)
;
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628097671050.png)
=
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162809801575.png)
﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162809837580.png)
;…
解答下面的問題:
(1)若n為正整數(shù),請你猜想
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628098731381.png)
=
_________;
(2)證明你猜想的結(jié)論;
(3)求和:
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162809909941.png)
+
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628099431024.png)
+
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628099781024.png)
+…+
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628100131994.png)
.
(1)解:
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628100491233.png)
;
(2)證明:右邊=
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162810084561.png)
﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162810122875.png)
=
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628101591646.png)
﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628101961470.png)
=
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628102331853.png)
=
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628102681387.png)
=左邊,
所以猜想成立.
(3)原式=1﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162810306573.png)
+
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162810342573.png)
﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162810378577.png)
+
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162810415577.png)
﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/20120816162810453587.png)
+…+
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628104891233.png)
﹣
![](http://thumb.zyjl.cn/pic1/upload/papers/c02/20120816/201208161628108181146.png)
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