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Thread: 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.
    $\displaystyle \lim_{n \to \infty}a_n = \frac{7+4n^2}{n+n^2}$

    To me it looks like a $\displaystyle \frac{\infty}{\infty}$ 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 $\displaystyle n$, 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

    $\displaystyle \lim_{n \to \infty}a_n = \frac{7+4n^2}{n+n^2}=$
    $\displaystyle \lim_{n \to \infty}a_n = \frac{\frac{7}{n^2}+4}{\frac{1+n}{n}}=$
    $\displaystyle \frac{0+4}{0}$ ?
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  4. #4
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    $\displaystyle \frac{{7 + 4n^2 }}
    {{n + n^2 }} = \frac{{\frac{7}
    {{n^2 }} + 4}}
    {{\frac{1}
    {n} + 1}}$
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  5. #5
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    Thank you.
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