二项式系数倒数级数恒等式

The Series of the Reciprocal of Binomial Coefficients

利用已知级数,通过裂项构造出一批新的二项式系数倒数级数,它们的分母分别含有1到4个奇因子与二项式系数的乘积表达式.所给出二项式系数倒数级数的和式是封闭形的.

Using one known series, we can structure several new series of reciprocals of binomial coefficients by splitting items. These denominators of series contains different the multiplication of 1 to 4 odd factors and combinatorial numbers. And some identities of series of numbers values of reciprocals of binomial 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.