I was plotting the relative error of the $e^{11/12 -n}n^{n+1/2}$ approximation to the factorial as $n$ gets larger and larger and at after some very large value of $n$ mathematica gives this plot:
Can somebody explain what exactly it means? Of course, I understand that for larger and larger $n$ the relative error tends to a value but I am not sure about how to interpret this graph. In particular, I don't understand how can the error be bigger for some $n$ than for some greater $n$.
Thanks.
Edit: I want to add that when $n$ is an order of magnitude less what I get is something like this: