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Math Help - Find the limit of the sequence

  1. #1
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    Find the limit of the sequence

    The problem says to find the limit of the sequence.

    an = (-1)n * (3n + e-n/5n)

    I'm not sure how to approach this problem. Do I use the ratio test?
    I apologize for the formatting. I'm not sure how to make the fraction look nice
    Last edited by NeedsHelpPlease; July 26th 2012 at 09:01 AM.
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  2. #2
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    Re: Find the limit of the sequence

    Quote Originally Posted by NeedsHelpPlease View Post
    The problem says to find the limit of the sequence.
    an = (-1)n * 3n + e-n/5n
    We cannot help if we cannot read the question.

    Is it (-1)^n(3)^n+\frac{e^{-n}}{5n}\text{ or }\frac{(-1)^n(3)^n+{e^{-n}}}{5n}~?
    Last edited by Plato; July 26th 2012 at 07:41 AM.
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  3. #3
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    Re: Find the limit of the sequence

    And the "ratio test" is a test for convergence of a series, not a sequence.
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  4. #4
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    Re: Find the limit of the sequence

    Actually there is a ratio test for sequences as well.

    For a sequence \displaystyle \begin{align*} \left\{ a_n \right\} \end{align*}, the ratio test states

    \displaystyle \begin{align*} \lim_{n \to \infty}\left| \frac{a_{n+1}}{a_n} \right| = L < 1 \implies \lim_{n \to \infty}a_n = 0 \end{align*}
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