# determine if a sequence converges/finding the limit

• Oct 27th 2009, 08:55 AM
mmattson07
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.
• Oct 27th 2009, 08:57 AM
Defunkt
Divide both numerator and denominator by the greatest power of $\displaystyle n$, the rest should be easy once you've done some basic limits..
• Oct 27th 2009, 09:10 AM
mmattson07
Ok so you would have

$\displaystyle \lim_{n \to \infty}a_n = \frac{7+4n^2}{n+n^2}=$
$\displaystyle \lim_{n \to \infty}a_n = \frac{\frac{7}{n^2}+4}{\frac{1+n}{n}}=$
$\displaystyle \frac{0+4}{0}$ ?
• Oct 27th 2009, 09:20 AM
Plato
$\displaystyle \frac{{7 + 4n^2 }} {{n + n^2 }} = \frac{{\frac{7} {{n^2 }} + 4}} {{\frac{1} {n} + 1}}$
• Oct 27th 2009, 09:22 AM
mmattson07
Thank you.