裂项法导出二项式系数倒数级数

The Series of Reciprocals of Binomial Coefficients Constructing by Splitting Terms

根据一个已知级数,使用裂项方法得到分母含有1到5个奇因子的二项式系数倒数级数,所给出二项式系数倒数级数的和式是封闭形的。并给出二项式系数数倒数值级数恒等式。裂项方法研究二项式系数变换是组合分析的新手段,也是产生新级数的一个初等方法。

Using one known series, we can structure several new series of reciprocals of binominal coefficients by splitting items. These denominators of series contains different the multiplication of one to five odd factors and binominal coefficients. And some identities of series of numbers values of reciprocals of binominal coefficients are given. The method of split items offered in this paper is a new combinatorial analysis way and a elementary method to construct new series.