Need help understanding/proving formal definition of limits

This is my first analysis class and I'm having trouble understanding how to prove these limits. Here's an example:

$\displaystyle a_{n}=\frac {1}{2n-3}$

Obviously, the sequence converges to 0. I'm just having trouble PROVING this using the formal definition, which states: A sequence $\displaystyle a_{n}$ converges to a real number A iff for each real number $\displaystyle \epsilon \geq 0$ there exists a positive integer n* such that

$\displaystyle |{a_{n}-A}| < \epsilon$ for all n $\displaystyle \geq$ n*.

Any help with this would be appreciated!