Proof of Limits: a^(1/n)

  • #1

Homework Statement


Let a>1. Prove the limit as n goes to [itex]\infty[/itex] of a1/n = 1.

The Attempt at a Solution


Given [itex]\epsilon[/itex] > 0, [itex]\forall[/itex]n>N, |a1/n-L|<[itex]\epsilon[/itex] and N=(a-1)/[itex]\epsilon[/itex].
|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).
 

Answers and Replies

  • #2
verty
Homework Helper
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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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