How to change style in a last a element in a nav bar?

Well, I'm a truly beginner with javascript, so I have trouble implementing even easiest DOM tricks with it. Actually I think I will place a very simple question here, but whatever, even this one makes me pull my hair out for all day long.

I got this horiz. navigation on my page:

<ul id="nav">
<li><a href="#">/home</a></li>
<li><a href="#">/services</a></li>
<li><a href="#">/staff</a></li>
<li><a href="#">/products</a></li>
<li><a href="#">/contact</a></li>
</ul>

The nav is dynamic and the list items can change through back end CMS. I have a separators for each of the menu items inserted through css. What I wanna do now is to actually get rid of the last a item separator through javascript. How can I do this? How can I select exactly the last a item from the nav, so I could be able to insert inner style which will delete it's separator "background:none"?

Thank you in advance!

 

var menuLinks;

if( document.getElementById('nav') && (menuLinks=document.getElementsByTagName('a')) )
 menuLinks[menuLinks.length-1].style.background='none';

Code (markup):

 

Thanks, but that doesn't work. Anyway I just found a working solution"

document.getElementById("nav").getElementsByTagName("LI")[(document.getElementById("nav").getElementsByTagName("LI").length)-1].firstChild.style.backgroundImage = "none";

Code (markup):

 

Just for the record that should have been:

var menuLinks, menu;

if( (menu=document.getElementById('nav')) && (menuLinks=menu.getElementsByTagName('a')) )
 menuLinks[menuLinks.length-1].style.background='none';

Code (markup):