Hi, I have a very simple example of 1/n converging to 0 (it cannot be solved using a limit, that would be very easy, we have to show it using the definition of the limit), but I don't know how to prove a more complex sequence using the definition of the limit.

The problem says:

"Using only the definition of the limit prove that the sequence a_n = (n^3-1)/(n^3+1) converges to 1."

I would really appreciate it if you could show me how to solve this, thanks a lot!