Well, maybe . . .
You may have audio difficulties, or at least I did. Save for the newest products from Apple the mini-DVI outputs only video, with a separate connection required for audio, thus the possible problem. If a new computer, never mind, the video and audio signals are combined from DVI, and you probably will not experience any issue connecting via HDMI to an HDTV. If not, then read on . . .
In attempting to connect a Black MacBook to a Sony HDTV I discovered that that putting video on the big screen was a fairly simple matter, and I never had any luck doing the same with audio. Video was a matter of an adapter for mini-DVI out/HDMI in. I used a mini-jack for audio out, adapted to white and red RCA plugs for audio in. But no matter which configuration I tried the audio would never work, even though the MacBook output it fine. What I discovered, at least with this Sony, is that it only accepts one input signal at a time, and apparently I was asking for two with separate video and audio inputs. However I could never get it to recognize the audio input on its own, so who knows.
Supposedly some people have successfully solved this dilemma, and if so they perhaps they will tell you exactly how. Just do not be surprised if it doesn't all go as smoothly as first expected. For the audio, one solution that would work is to bypass that of the HDTV and use a separate sound system; it would work, and with better sound in any event.
For the video, it was about as simple as connecting the cable and choosing the appropriate input on the HDTV. But you will probably need to use the HDTV menu to change the picture aspect ratio to utilize the full screen. I did. Elsewhere you might read descriptions of exactly how this is done, but know every HDTV has its own nomenclature, so your sets menu may be slightly different.
By the way, the video looked perfectly fine on the big screen. Good luck.