一类线性递归数列通项公式的证明和应用

Prove and Application of Sequences General Term Equation

利用线性代数知识,证明且给出下列形式的数列通项公式的一种求法:an+m=kman+(m-1)+…+k2an+1+k1an,其中k1,k2,…,km为已知常数,数列的前m项a0,a1,…,am-1已知。并用这种方法求出了斐波那契数列的通项公式。

In this paper, we proved a new algorithm for solving constant coefficient recursive sequences general term equation through matrices calculation, and applied the method to solve this problem.