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

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.