Should I sell my 18-55mm and 55-200mm lenses and purchase an 18-200mm lens?

I have the 18-55mm kit lens that came with my camera, as well as a 55-200mm lens I got as a gift one year. I know that Nikon sells an 18-200mm lens. I was wondering if I would be better selling my two lenses and purchasing this single lens that combines the two zoom lengths. I find it somewhat inconvenient having to switch between lenses when I want to take a shot of something far away, and then wanting a wide angle of the scenery or something like that.
So I was just wondering if selling those other two lenses and buying the one would be worth the effort?

I would keep the combo of two lenses and change between them. I find 18-200 a little too heavy for placing it on my camera and it's way more expensive.

Only if you want neck-strain.

Back in the day, my friends and I used to change lenses, blindfold, against the clock (none of us trusted zooms, so we used prime lenses on our MF SLRs) because you could never be certain you'd have the necessary lens fitted when required - I can still change lenses in a matter of seconds - a skill that seems sadly lacking these days

The 18-200 is a bit of a compromise lens, and in reality no better or no worse than what you already have.

I used to own this lens, and I used it as an all-in-one lens for vacation. But then I upgraded my "normal" lens to a 17-50mm f/2.8 when I bought the D7100, and found I rarely used the 18-200.

Here is a review that compares the combo of the 18-55mm and 55-200mm to the 18-200mm lens. You will find that neither lens combination is perfect.

http://www.althephoto.com/lenses/super-zooms.php

All three lenses do have some optical issues at certain focal lengths. But they are average for consumer-grade lenses. You are not improving your optical quality by going with the 18-200mm, just cutting down on one lens.

If you want a better lens, consider buying the Sigma 17-50mm f/2.8 to replace your 18-55mm, and when the funds allow, buy either a Sigma 50-150mm f/2.8 or 70-200mm f/2.8 to replace the 55-200mm.

Yes if you want to do it all with just one lens.

No if you understand what optical quality means.