Will a sigma 50-200mm lens fit a nikon d3100?

Http://www.sigma-imaging-uk.com/lenses/dclenses/50-200mm.htm.
http://www.currys.co.uk/...9-pdt.html

Sure just make sure you get it in a Nikon mount.

Will it fit? - Yes. There's a Nikon mount version of this lens.

Will it focus? - Yes. This lens is an HSM lens, thats the equivalent of AF-S.