﻿ 裂项法导出二项式系数倒数级数

# 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

Abstract: 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.

[1] B. Sury, T. N. Wang and F.-Z. Zhao. Some identities involving of binomial coefficients. Journal of Integer Sequences, 2004, 7: Article ID: 04.2.8.

[2] J.-H. Yang, F.-Z. Zhao. Sums involving the inverses of binomial coefficients. Journal of Integer Sequences, 2006, 9: Article ID: 06.4.2.

[3] S. Amghibech. On sum involving Binomial coefficient. Journal of Integer Sequences, 2007, 10: Article ID: 07.2.1.

[4] T. Trif. Combinatorial sums and series involving inverses of binomial coefficients. Fibonacci Quarterly, 2000, 38(1): 79-84.

[5] F.-Z. Zhao, T. Wang. Some results for sums of the inverses of binomial coefficients, integers. The Electronic Journal of Combinatorial Number Theory, 2005, 5(1): A22.

[6] R. Sprugnoli. Sums of reciprocals of the central binomial coefficients, integers. The Electronic Journal of Combinatorial Number Theory, 2006, 6: A27.

[7] 及万会, 张来萍. 关于正负相间二项式系数倒数级数[J]. 理论数学, 2012, 2(4): 192-201.

[8] I. S. Gradshteyn, I. M. Zyzhik. A table of integral, series, and products (7th Edition). Burlington: Academic Press, 2007: 56, 61.

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