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

1. ## 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.

2. Divide both numerator and denominator by the greatest power of $n$, the rest should be easy once you've done some basic limits..

3. Ok so you would have

$\lim_{n \to \infty}a_n = \frac{7+4n^2}{n+n^2}=$
$\lim_{n \to \infty}a_n = \frac{\frac{7}{n^2}+4}{\frac{1+n}{n}}=$
$\frac{0+4}{0}$ ?

4. $\frac{{7 + 4n^2 }}
{{n + n^2 }} = \frac{{\frac{7}
{{n^2 }} + 4}}
{{\frac{1}
{n} + 1}}$

5. Thank you.