Do i need a sigma 70-200mm?

I'm a beginner and I have a Nikon D3100 and the Nikkor 55-300mm f/4.5-5.6, I was wondering do I need the sigma 70-200mm f/2.8?

Absolutely! Then nobody will know you're a beginner.

You already have a telephoto lens AND you're a beginner. At this early stage, don't buy lenses that just do what your existing lenses already do. And you need some time to figure out what types of lenses you actually need based on the types of photos you like to take. I once planned to get a telephoto lens but discovered that I never actually wanted to take a picture that needed such a lens. I'm not shooting horse races or anything, after all.

It's simple math. Look at the numbers. 70-200mm is within 55-300mm. Do you understand now?

If you are after a fast lens (low f/number) I suggest you get the 50mm f/1.8.It's cheaper and a whole lot faster!