How to Prove the Limit as n Goes to Infinity of a^(1/n) = 1

major_maths · Oct 4, 2011

Homework Statement

Let a>1. Prove the limit as n goes to \infty of a^1/n = 1.

The Attempt at a Solution

Given \epsilon > 0, \foralln>N, |a^1/n-L|<\epsilon and N=(a-1)/\epsilon.
|a^1/n-L| = a^1/n-1

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

verty · Oct 4, 2011

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.

How to Prove the Limit as n Goes to Infinity of a^(1/n) = 1

Homework Statement

The Attempt at a Solution

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