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How can I prove that $ \{ n^{1/n} \}_{ n \in \mathbb{N}} $ is a decreasing sequence after some $n_0 \in \mathbb{N} $; and also find out such $n_0$?

Thanks in advance.

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    Consider the behavior of the function $f(x) = x^{1/x}$.2012-12-18
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    Use $y=\frac{lnx}{x}$2012-12-18

4 Answers 4