# Proof of Limits: a^(1/n)

1. Oct 4, 2011

### major_maths

1. The problem statement, all variables and given/known data
Let a>1. Prove the limit as n goes to $\infty$ of a1/n = 1.

3. The attempt at a solution
Given $\epsilon$ > 0, $\forall$n>N, |a1/n-L|<$\epsilon$ and N=(a-1)/$\epsilon$.
|a1/n-L| = a1/n-1

...and that's where I get confused. I know that I have to multiply (a1/n-1) by something but I'm not sure what exactly (a hint my professor gave).

2. Oct 4, 2011

### verty

Here's a hint that may or may not help. You want |a^(1/n) - 1| < e. So for example, perhaps you want |a^(1/n) - 1| = e/2.

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