Sequence Problems

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October 5th 2009, 07:52 AM
matt.qmar

Sequence Problems

Hi there! have a few problems with some sequence questions!
Does the sequence from 1 to infinity of
$\frac{4^{(n-1)}+3^{(n+1)}}{5^n}$
converge or diverge?

similarily for the sequence from 1 to infinity of
$(\frac{1}{n})^{(\frac{1}{n})}$

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!
October 5th 2009, 08:14 AM
Plato

If you have more than one character in an exponent, set off the whole exponent in braces.
[tex]4^{(n+1)}[/tex] gives $4^{(n+1)}$ instead of $4^(n+1)$ .
October 5th 2009, 11:34 AM
matt.qmar

Thank you! Looks like it is meant to look now.
October 5th 2009, 12:04 PM
Plato

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

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