变系数非线性递归序列的极限

On the Limit of a Kind of Nonlinear Recurrent Sequences With Variable Coefficients

对形如F_(n+p)=(sum from to i=1 to p)a_i(n)F_(n+i-1)^(b_i),n≥1的变系数非线性递归序列{F_n}的极限问题进行了研究,给出了在满足一定条件时,序列{F_n}收敛且极限值与初始值F_i>0,i=1,2,…,p无关.

In this paper, we study the limit of a kind of nonlinear recurrent sequences withvariable coefficients Fn＋p=∑ i=1^pai（n）F^bi n＋i-1,n≥1.We prove that ,under a certain condition,the sequence of {Fn} is convergenct,and its limit value does not depend on the initial value Fi〉0,i=1,2,…,p.