The main purpose of this paper is to prove that under some conditions, if for a real number ,

which will allow us to establish a discrete version of the L’Hôpital rule; a powerful tool to show the convergence of sequence of real numbers. We will also use this version of the L’Hôpital rule to infer the Stolz-Cesàro theorem. Finally, we will present a series of examples to illustrate the utility of this version of the  L’Hôpital rule.