引用:
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作者: newagedreams
0.999... is already a limit, so the limit is 1 means the limit equals 1.
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那是不是所有循環小數都可以化成 limit 再找它相應的分數...?
例如 0.343434...:
0.343434...
=lim(n->INF) (0.31 + 0.31*0.1 + 0.31 *0.1^2 + ... + 0.31*0.1^n)
=0.31*lim(n->INF) (1 + 0.1 + 0.1^2 + 0.1^n)
=0.31*lim(n->INF) (1 - 0.1^n)/(1 - 0.1)
=0.31/0.9 = 31/90
不過 31/90 = 0.3444...
我的計算有什麼問題...?
