Identities involving rational sums by inversion and partial fraction decomposition

Abstract

Identities appearing recently in: J. L. Diaz-Barrero, J. Gibergans-Baguena P. G. Popescu: Some identities involving rational sums. Appl. Anal. Discrete Math., 1 (2007), 397-402, are treated by inverting them; the resulting sums are evaluated using partial fraction decomposition, following Wenchang Chu: A binomial coefficient identity associated with Beukers’ conjecture on Apery numbers. Electron. J. Combin., 11 (1): Note 15, 3 pp. (electronic), 2004. This approach produces a general formula, not only special cases.