id ilke to know if the upgrade to virtual dj pro (full please, not 20 days) is free or not with the serial number given with the rmx2?

This information is available on the VDJ website:

http://www.virtualdj.com/buy/index.html

if you already own an Atomix Productions' software

If you own another product sold by Atomix Productions or one of its partners, you can upgrade to VirtualDJ Pro Full at a discounted price; (for example, products that qualify for upgrade pricing include VirtualDJ Pro Basic, VirutalDJ HomeEdition 5, VirtualDJ Limited Edition (LE), Numark Cue or VirtualVinyl, etc...)

You will then be a full member of the VirtualDJ Community, and enjoy all the advantages of VirtualDJ Pro Full.
You will get the latest versions before everybody else, and benefit from the most advanced features and the broadest range of compatibility.