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Math Help - Sequence Problems

  1. #1
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    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!
    Last edited by matt.qmar; October 5th 2009 at 11:35 AM.
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  2. #2
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    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) .
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  3. #3
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    Thank you! Looks like it is meant to look now.
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  4. #4
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    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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