ON THE SPEED OF CONVERGENCE OF THE SEQUENCES

The study of any nontrivial convergence of a sequence of real numbers conducts to the problem of finding the limit but also to the problem of the speed of this convergence. This speed of convergence is characterized by the first iterated limit (that supposes the existence of a function of natural variable that tends to zero for n tending to infinity, a function that appears as the first term of a sequences of such functions). A significant characterization of the first iterated limit may be given by a two sided estimate, from which the first iterated limit results immediately.