determine if a sequence converges/finding the limit

**mmattson07** · October 27th 2009, 08:55 AM

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.

**Defunkt** · October 27th 2009, 08:57 AM

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

**mmattson07** · October 27th 2009, 09:10 AM

Ok so you would have

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