Determine if the sequence {(2n-1)/(3n^2+1)} n=1,2,3.... converges or diverges. If the sequence converges find its limit.

I did L'Hopital's rule to find the limit which I found to be 2/infinity= 0. Is this correct? Would that mean that the sequence converges. Would this also mean that the limit is 0?

Thanks in advance.