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Convergence of Sequence: (n^2)/(e^n)

  1. Mar 28, 2012 #1
    NEVERMIND! IT IS 0! I SOMEHOW WAS STARING AT THE WRONG ANSWER SHEET FOR A LITTLE BIT! THANK YOU!

    1. The problem statement, all variables and given/known data

    Determinte whether the sequence converges or diverges:
    (n^2)/(e^n)


    2. Relevant equations

    The book says that the solution is: e/(e-1).

    However, the limit of the equation y=(n^2)/(e^n) as n goes to infinity is 0.

    I don't know why I can't seem to apply the theorem that:

    If the limit as x goes to infinity of f(x) = L and f(n)= an, then the limit of an as x approaches infinity is L.

    3. The attempt at a solution

    I used L'Hôpital's rule to prove the limit is 0. Wolfram alpha confirms this.
     
    Last edited: Mar 28, 2012
  2. jcsd
  3. Mar 28, 2012 #2

    LCKurtz

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    The question is whether the sequence converges, so the answer would be yes or no, right? What question does your book say e/(e-1) is the answer to? You are correct that the sequence converges to 0. Have you stated the question fully?
     
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