１引言有关三角数列和、积恒等式的证明问题，在现行高中数学教材中是用数学归纳法证明的，当然数学归纳法是证明这类恒等式的基本方法，但是过程比较繁琐．本文给出一种简洁的证明方法，它可以作为证明数列恒等式的通法．２两个定理定理１如果ｆ（ｎ）－ｆ（ｎ－１）＝ｇ... I. INTRODUCTION Proof of trigonometric series and product constant equation is proved by mathematical induction in current high school math teaching materials. Of course, mathematical induction is the basic method to prove this kind of identity, but the process is complicated. This paper presents a succinct method of proof that can be used as a general method of proof of identity. 2 Theorems Theorem 2 If f (n) -f (n-1) = g