What would be a good nikon lens for sporting events?

If I purchase the Nikon d3000 is the Extra lens 55-200 a good lens.

The 55-200 mm is a good length lens for shooting field sporting events during the day. Nikon has a new 55-300 mm lens that will give you better reach and you may like better.

Here is what a 300 mm lens can do when shooting football.

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As you can see, it gets close up to the action from the sidelines.

As you notice this was shot under the lights with a much faster 300 mm f/2.8 prime lens so is only shown to illustrate how close to the action you can get at 300 mm.

With the crop factor on the Nikon the 55-200 becomes effectively a 300mm at the longest length and the 300 would be 450mm! In this case you might want a) a tripod, b) a VR version of the lens and c) lots of light as they're f/5.6 at the longest end.

You might also want to consider the Sigma and Tamron 70-300mm lenses

I would favor the 75-300 VR over the 55-200 for this application.

I would consider Nikon 55-200mm f/4-5.6G ED IF AF-S DX VR [Vibration Reduction] Nikkor Zoom Lens

55-200mm zoon Nikkor lens with f/4-5.6 maximum aperture for Nikon digital SLR cameras
2 extra-low-dispersion (ED) glass elements for minimized chromatic aberration and superior optics
Super-integrated coating minimizes ghosting and flare for more vivid images in dim lighting
Silent Wave Motor produces quick and quiet high-speed autofocusing; weighs 9 ounces
Measures 2.7 inches in diameter and 3.1 inches long; 5-year warranty