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Math Help - Another quick series question

  1. #1
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    Another quick series question

    If a series is
    <br />
a_n > 0 \quad \text{ for every } n<br />

    And converges must there be a N such that ?

    <br />
\frac{a_{n+1}}{a_n} < 1 \quad \text{ for every } n\geq N<br />

    Does this hold in general?
    Last edited by hjortur; October 2nd 2009 at 03:53 PM.
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  2. #2
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    Quote Originally Posted by hjortur View Post
    If a series is
    a_n > 0 \quad \text{ for every } n
    Is there a N such that ?
    \frac{a_{n+1}}{a_n} < 1 \quad \text{ for every } n\geq N
    Does this hold in general?
    This may well be a problem in language or translation.
    I don’t know what the above quote means.
    Consider this, a_n=\frac{1}{n} satisfies that condition.
    So what exactly does you question mean?
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  3. #3
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    Yeah, sorry, I noticed now that I deleted "if series is convergant" when I was formatting the message

    Fixed
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  5. #5
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    I was just having a trouble with one proof on my assignment.
    If the statement from my post were true it would have made my life a heck of a lot easier.
    Well, after thinking about this I concluded that this was indeed false.
    But it doesn't matter, I figured out how to write my proof using the limit
    comparison test.
    I am not going to post the question here, I am not sure about my
    university's standpoint on asking for help with homework on this forum.
    Thanks for the link
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