Will this lens fit on my nikon d3100?

Http://www.currys.co.uk/gbuk/nikon-ed-af-s-dx-nikkor-55-200-mm-f-4-5-6g-telephoto-zoom-lens-00734639-pdt.html

Yes it will and as it's an AF-S lens it will also autofocus with your D3100

Yes it will. Any Nikon AF-S lens will fit and auto-focus on the D3100. Non AF-S lenses will fit but will only manual focus.
This will show you lenses compatible with your D3100 http://lenshero.com/nikon-lens-compatibility

It will fit.

It is also an AF-S lens so you will get full functionality.

I'm fairly certain every Nikon lens made since the 50s fits on every Nikon DSLR, they all have the same mount. The only possible trouble comes with what parts of the lens are useable. The D3000 and D5000 range like yours do not have anything to read AI lenses or use the AF on screw-type AF lenses, known as AF-D.

AI lenses were made until partway through the 80s I think but there are still a rare few sold today. These will technically work on beginner cameras but the camera won't detect it as a lens so it will only work in manual mode without autofocus (these lenses have no autofocus anyway). Metering (which tells you how exposed your image will be with your current settings) will not work, and neither will the focus detection system which tells you when the subject your focus point is on is in focus.

AF-D lenses are still made today but are not as common as AF-S lenses. These lenses have an autofocus system that is inside some cameras (but not yours) and connects to the lens with a little screw. So these lenses won't autofocus on your camera but everything else will work.

All AF-S lenses work in every way on every Nikon DSLR. The lens you are talking abot is AF-S, as are most lenses sold today. The autofocus motor is inside the lens so it doesn't need the screw that the more expensive cameras have and are generally better at autofocusing too.

It's usually easy to tell AF-S and AF-D lenses apart at a glance, they have very different design aesthetics and the AF-D lenses also usually have an aperture ring which means aperture control is on the lens, not the camera.

If you are buying non-Nikon lenses, it's good to check what type of autofocus it has, but most of them are also AF-S.