高阶等差级数的一些理论及其应用

On the Systematic Discussion to Higher Arithmetic Progression

通过引进组合学里的一些新的符号运算和定理,较为系统和严格地论述和证明了高阶等差级数的理论基础.在此基础上,就某种情形阐述其具体的一些应用方法.最后论述了与高阶等差级数相关联的一类级数——混合级数在有限和无穷时的求和问题.

In this paper,by introducing some new symbolic operations and theorems in combinatorial mathematics,the foundation of arithmetic progression of higher-order is discussed and proved through a more systematic and rigorous way.On this basis,to some situation,some of the specific application methods are described.Lastly,a sort of series associated with arithmetic progression are discussed—mixed series under the questions of finite and infinite summation.