The Series of Reciprocals of Non-central Binomial Coefficients

Laiping Zhang, Wanhui Ji

Yinchan Energy College, Yinchuan, China.

DOI: 10.4236/ajcm.2013.33B006                

Abstract

Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.

Keywords

Binomial Coefficients; Split Terms; Reciprocals; Series; Non-central; Closed Form

Conflicts of Interest

The authors declare no conflicts of interest.

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