(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the following limit:

[tex]lim_{n \rightarrow \infty } n^{ 1 / n } = 1 [/tex]

2. Relevant equations

Not sure.

3. The attempt at a solution

Given any [tex]\epsilon > 0[/tex], choose [tex]N \in \mdseries N[/tex] s.t.

[tex]\left| n^{ 1 / n } - 1 \right| < \epsilon[/tex] for all [tex]n > N[/tex]

I am not sure how to proceed.

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# Proving limit of the nth root of n

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