- #1

- 11

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## Homework Statement

Prove the following limit:

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

## Homework Equations

Not sure.

## 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.