I have some problems with this, because this sequence could converge to some point, or goes to infinity, only this two possibilities, and really I don´t know how to prove that no other possibility can happen, that´s my problem. The sequence is such that exist a fixed positive constant C, such that for every m,n integers $ a_m + a_n < a_{m + n} + C $
prove that $ (a_n)/n $ converge to a point, or goes to infinity $
and some idea to prove in general that other of two possibilities can´t happen?