Proving Limit of r/n as n Approaches Infinity

[gtfitzpatrick]

Homework Statement

prove that lim_{(n\rightarrow\infty)}(r^1/n) = 1 for r> 0

The Attempt at a Solution

let \epsilon > 0 be given we need to find n₀ \in N such that

\left|r^1/n - 1 \left| < \epsilon

but not really sure where to go from here?

 

[grief]

What if the problem was a little simpler -- proving that the limit as n approaches 0 of r^n equals 1. How would you go about doing that?

 

[gtfitzpatrick]

1 < L \leq r^1/n

implies

1\leq Lⁿ \leq r

i'm not sure how this follows?