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Math Help - [SOLVED] Monotone Sequence

  1. #1
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    [SOLVED] Monotone Sequence

    Using A_{n+1}/A_n
    [ne^{-n}]_{n=1}
    ive got to
    \frac {(n+1)e^{-(n+1)}}{ne^{-n}}
    but dont know how to simplify from there
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by vinson24 View Post
    Using A_{n+1}/A_n
    [ne^{-n}]_{n=1}
    ive got to
    \frac {(n+1)e^{-(n+1)}}{ne^{-n}}
    but dont know how to simplify from there
    Please repost this with a clearer explanation.

    CB
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  3. #3
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    ne^{-n}is the sequence n=1 to infinity
    and they want me to find out if its strictly increasing or strictly decreasing using ratio of successive terms

    I have gotten this far \frac {(n+1)e^{-(n+1)}}{ne^{-n}}
    but not sure how to simplify this to show that this is greater or less than 1. I know the answer is strictly decreasing but not sure how to simply the ratio to prove that
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by vinson24 View Post
    ne^{-n}is the sequence n=1 to infinity
    and they want me to find out if its strictly increasing or strictly decreasing using ratio of successive terms

    I have gotten this far \frac {(n+1)e^{-(n+1)}}{ne^{-n}}
    but not sure how to simplify this to show that this is greater or less than 1. I know the answer is strictly decreasing but not sure how to simply the ratio to prove that
    \frac {(n+1)e^{-(n+1)}}{ne^{-n}}=\frac{(n+1)e^{-1}}{n}=e^{-1}+\frac{e^{-1}}{n}

    CB
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