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1/9 = 0.111 ....
2/9 = 0.222 ....
3/9 = 0.333 ....
4/9 = 0.444 ....
5/9 = 0.555 ....
6/9 = 0.666 ....
7/9 = 0.777 ....
8/9 = 0.888 ....
9/9 = 0.999 ..........   <------ ???

無窮等比級數 :  0.999...=0.9+0.09+0.009+0.0009+...
                      首項是0.9，公比為0.1的無窮等比級數
                              
其和就是(首項)/(1-公比)=0.9/(1-0.1)=1

So 9/9 = 0.999 ... = 1               <------ ???

yes.
http://hk.geocities.com/mathsworld2001/themes/9and1.htm

P.S. Do you afraid of SARS? 景棉樓有人出事

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P.S. Do you afraid of SARS? 景棉樓有人出事

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1/3=0.33333333333333333333.........

(1/3)X3=1

0.33333333333333333333333.....X3=0.99999999999999999999999....

所以0.999999999999999999999.....=1

也可以這樣證吧?

是,
0.9999999......可以使用級數表示

此級數收歛後即為1

有一種證明方法，我覺得還不錯


令0.999999999999999999999999999999.....................=S

則
10S-S=9.999999999999999999999999........................-0.99999999999999999999999...........................
         =9

又10S-S=9S=9
所以S=1