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Math Help - converging with e

  1. #1
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    converging with e

    problem is: An = ( (e^2n)/(n^2 +3n - 1) )

    my question is: Can i decide what number this problem is converging to by dividing the top and bottom of this equation by the largest n in the denominator? By doing that, what does this determine? just a guess?

    Also, I'm unsure how to convert the natural log to something I can work with.

    could i do this first --> 2n ln(e) --> 2n (1) --> so 2n?

    this problem diverges, btw.

    -thanks for any help.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    problem is: An = ( (e^2n)/(n^2 +3n - 1) )

    my question is: Can i decide what number this problem is converging to by dividing the top and bottom of this equation by the largest n in the denominator? By doing that, what does this determine? just a guess?

    Also, I'm unsure how to convert the natural log to something I can work with.

    could i do this first --> 2n ln(e) --> 2n (1) --> so 2n?

    this problem diverges, btw....

    Hello,

    this is only a try, maybe it helps nevertheless:

    \lim_{n \rightarrow \infty}{\left( \frac{e^{2n}}{n^2+3n-1} \right)} simplifies for very large number n to:

    \lim_{n \rightarrow \infty}{\left( \frac{e^{2n}}{n^2} \right)}=\lim_{n \rightarrow \infty}{\left( \frac{e^{n}}{n} \right)^2} = \left( \lim_{n \rightarrow \infty}{ \frac{e^{n}}{n}} \right)^2

    And as you may know the limit \lim_{n \rightarrow \infty}{ \frac{e^{n}}{n}} doesn't exist, that means A_n diverges.

    EB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by rcmango View Post
    problem is: An = ( (e^2n)/(n^2 +3n - 1) )

    my question is: Can i decide what number this problem is converging to by dividing the top and bottom of this equation by the largest n in the denominator? By doing that, what does this determine? just a guess?

    Also, I'm unsure how to convert the natural log to something I can work with.

    could i do this first --> 2n ln(e) --> 2n (1) --> so 2n?

    this problem diverges, btw.

    -thanks for any help.
    The thing you need to know to make this easy is that e^x increases faster than any polynomial in x, so A_n \to \infty as n \to \infty.

    Alternativly you can use L'Hopitals's rule twice to discover the same result.

    RonL
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