Originally Posted by

**Shizaru** Starting to look at Convergence of sequences and given an example without a solution. The solution would really help my understanding of what's going on here:

$\displaystyle x_{n} = \frac{9n^{3}+3}{2n^{3}+5}$

Define what is meant by saying $\displaystyle x_{n}$ converges to the limit l as n goes to infinity. Show that $\displaystyle x_{n}$ converges to $\displaystyle \frac{9}{2}$ as n tends to infinity.

Now I know you can pull out the fraction and show that the rest tends to 1 (right?), simple enough you can already see the $\displaystyle \frac{9}{2}$ right there but how do you show this? Basically that l = $\displaystyle \frac{9}{2}$