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I was messing around in IRB and I decided to make a $n^{th}$ root function and noticed that for very large roots of numbers, the answer always converges to $1$. It has been a while since I have done any work with infinite series but could someone explain why this is, or offer a proof. (The most similar thing I could think of is the proof of $.9$ repeating equaling $1$)

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    The list of numbers you get by taking the $n^{th}$ root for increasing values of $n$ is called a sequence and not a series.2012-05-17
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    Let's say of any *positive* number for sake of definition.2012-05-17

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