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stability; periodic solution; difference equation
In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence \[ x_{n+1}=\frac{a_{0}x_{n}+a_{1}x_{n-1}+\dots +a_{k}x_{n-k}}{b_{0}x_{n}+b_{1}x_{n-1}+\dots +b_{k}x_{n-k}},\,\,\,n=0,1,\dots \,\ \] where the parameters $ a_{i}$ and $b_{i}$ for $i=0,1,\dots ,k$ are positive real numbers and the initial conditions $x_{-k},x_{-k+1},\dots ,x_{0}$ are arbitrary positive numbers.
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