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In this paper the asymptotic stability of equilibria and periodic points ofthe following higher order rational difference Equation x_{n+1} =(alphax_{n-k})/(1+x_{n}...x_{n-k}), k>=1, n=0,1,... is studied where the parameters?alpha, betta, and gamma are positive real numbers, and the initial conditionsx_{-k}, ..., x_{0} are given arbitrary real numbers. The forbidden set of thisequation is found and then, the order reduction method is used to facilitatethe analysis of its asymptotic dynamics

Stability and convergence of a higher order rational difference Equation