Limit of Sequence: Convergent, Limit = 1

[Jolteon]

Homework Statement

Determine if the following sequence in convergent or divergent, and state the limit if it converges.

((4^n)/n)^(1/n) or "The nth root of '4 to the n' over 'n'"

Homework Equations

lim ___(n)^(1/n) = 1
n->inf

The Attempt at a Solution

I had this question on a quiz earlier, but wasn't too sure about my answer. As n approaches infinity, the exponent on the very outside approaches 0. So naturally I thought that anything to the 0 is 1. However, thinking back on it, I think the inside gets larger faster than the outside exponent gets smaller. Thanks for any help, I don't want to wait until Monday!

 

[vela]

Try using the property

$$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$

and then the limit you noted.