用母函数法推导斐波那契数列的通项公式

Derivation of the Common Term Formula Fibonaci's Seguence by Generating Function

递推数列的通项公式的求解近年来吸引了许多数学工作者的注意,目前已经出现了诸如数学归纳法、特征方程法、待定系数法等求解方法。受齐次线性微分方程的母函数解法的启发,研究人员利用母函数,力图寻找出著名的斐波那契数列通项公式的一种新的求解方法.

The solution of the common term formula of the recurrence sequence recently has attracted much attention from mathematics researchers,and some methods has been given successfully such as mathematical induction,speciality equation,undetermined coefficient method,and so on.Enlightened from the solution of the generating function for omogenous linear differential equations,researchers try to find a new solution for the general term formula of Fibonaci＇s seguence by application of the generating function.,