
Sequence Problems
Hi there! have a few problems with some sequence questions!
Does the sequence from 1 to infinity of
$\displaystyle \frac{4^{(n1)}+3^{(n+1)}}{5^n}$
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!

If you have more than one character in an exponent, set off the whole exponent in braces.
[tex]4^{(n+1)}[/tex] gives $\displaystyle 4^{(n+1)} $ instead of $\displaystyle 4^(n+1) $.

Thank you! Looks like it is meant to look now.

Take notice that $\displaystyle \frac{{4^{n  1} + 3^{n + 1} }}{{5^n }} = \frac{1}{4}\left( {\frac{4}{5}} \right)^n + 3\left( {\frac{3}{5}} \right)^n $.
If you mean sequence then the limit is zero.
If you mean series then this is the sum of two geometric series both converge.