牛顿公式的两种证明及应用

Two Proofs and Applications of Newton Formula

摘要: 本文首先对牛顿(Newton)公式的两种主流证明方法——多项式的比较系数法和数学归纳法进行总结。其次，对一个条件恒等式进行反思探究，利用牛顿公式对其推广，从理论上给出一类等次幂和式的证明，最终得到了新的命题。

Abstract: This paper first summarizes two mainstream methods of proving Newton Formula—the method of comparing coefficients of polynomials and the method of mathematical induction. Next, a conditional constant equation is explored reflectively, and its generalization using Newton Formula is used to give a theoretical proof of a class of equal powers and equations, which eventually leads to a new proposition.