关于多项式数列求和问题的研究

The Study on the Issue of Summation of Polynomial Series

多项式数列求和问题是数学中比较基础的问题。本文利用组合式求和公式，使用待定系数法，较好地解决了通项为多项式的数列求前n项和的问题。本文推导了通项为组合式的求和公式，证明了任意多项式数列求前n项和的可行性，并给出了几个实例。与现有方法相比较，本方案不仅方法简单，而且使用数学知识容易掌握，应用方便。

The issue of summation of polynomial series is the basic problem in mathematics. The paper solves the problem of summation of former n terms as to series with general term as polynomial by means of combined summation formula and the method of undetermined coefficient. The paper deduces the summation formula of combined general term, proves the feasibility of summation of former n terms as to arbitrary polynomial series and gives some examples. Compared with the current methods, this program is not only simple, but convenient in using the basic knowledge of mathematics.