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?