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Math Help - determine if a sequence converges/finding the limit

  1. #1
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    determine if a sequence converges/finding the limit

    Hey I have the problem

    Determine whether the sequence converges or diverges. If it converges, find the limit.
    \lim_{n \to \infty}a_n = \frac{7+4n^2}{n+n^2}

    To me it looks like a \frac{\infty}{\infty} situation and doesn't converge but do i have to do some algebraic manipulation to be able to take the limit and find what it converges to? Thanks.
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  2. #2
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    Divide both numerator and denominator by the greatest power of n, the rest should be easy once you've done some basic limits..
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  3. #3
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    Ok so you would have

    \lim_{n \to \infty}a_n = \frac{7+4n^2}{n+n^2}=
    \lim_{n \to \infty}a_n = \frac{\frac{7}{n^2}+4}{\frac{1+n}{n}}=
    \frac{0+4}{0} ?
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  4. #4
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    \frac{{7 + 4n^2 }}<br />
{{n + n^2 }} = \frac{{\frac{7}<br />
{{n^2 }} + 4}}<br />
{{\frac{1}<br />
{n} + 1}}
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  5. #5
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    Thank you.
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