Hi there! have a few problems with some sequence questions!

Does the sequence from 1 to infinity of

$\displaystyle \frac{4^{(n-1)}+3^{(n+1)}}{5^n}$

converge or diverge?

similarily for the sequence from 1 to infinity of

$\displaystyle (\frac{1}{n})^{(\frac{1}{n})}$

For the latter, I have it out to the lim (n to infinity) of (1/n)(ln 1 - ln n) = ln L where L is the original limit, not sure if that is the correct direction to be heading, or if I am already finished? it seems like an indeterminate form?

Thank you!