How can I connect my PSP 3001 to my TV?
The PSP component cables labelled "for 2000 series only" were produced before the 3000 series PSP models came out. At the time they were released this was the same thing as saying "doesn't work with 1000 series models". In fact these cables will also work 3000 series models as well, as these newer models also support AV-out using the same connector. The cables don't work with the original "fat" 1000 series models because these original models don't support video output through any sort of cable.
Note make sure to get a component cable with 5 RCA jacks (3 video, 2 audio) and that your TV has a component input that you can connect it to. While composite and S-Video PSP cables exist they don't work when playing PSP games.