关于正负相间二项式系数倒数级数

On Series Alternated with Positive and Negative Involving Reciprocals of Binominal Coefficients

摘要: 利用已知级数，通过裂项构造出一批新的正负相间二项式系数倒数级数，它们的分母分别含有1到5个奇因子与二项式系数的乘积表达式。所给出正负相间二项式系数倒数级数的和式是封闭形的。并给出正负相间二项式系数数倒数值级数恒等式。裂项的方法研究二项式系数倒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。

Abstract: Using one known series, we can structure several new alternated with positive and negative 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 an elementary method to construct new series.