Can this: NIKON AF 75-240MM 1:4.5-5.6 D ZOOM LENS type of lens be used on a Nikon D3100?

Http://www.ebay.com/itm/261122022363

This is an AF lens, not an AF-S, which means the lens does not have a built in focus motor. It will work on your camera in manual focus, but not auto because your camera body doesn't have a focus motor. If you want auto focus, you need to look for AF-S models

The lens is obviously compatible with D3100. But, You must consider 2 points when using such high zoom lens.

1.IT MUST BE VR (Vibration Reduction) Lens, not ED. Because, when your focal length will be higher, small shake in your hand will blur the image. VR lens will automatically adjust it.

2.It should be AF-S. In AF-S lens, you will get auto focus option. You need it because D3100 body don't have built in auto focus motor. Manual focusing is obviously possible, but, in is really tough when you will snap with a high focal length.