# Sequence limits

1. Dec 8, 2009

### gtfitzpatrick

1. The problem statement, all variables and given/known data

prove that lim(n$$\rightarrow\infty$$)(r1/n) = 1 for r> 0

3. The attempt at a solution

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

$$\left|$$r1/n - 1 $$\left|$$ < $$\epsilon$$

but not really sure where to go from here?

2. Dec 8, 2009

### 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?

3. Dec 9, 2009

### gtfitzpatrick

1 < L $$\leq$$ r1/n

implies

1$$\leq$$ Ln $$\leq$$ r

i'm not sure how this follows?