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06092212 Chu, Wenchang Wang, Xiaoxia Recurrence relations of the second order and infinite series identities. Ars Comb. 101, 449-457 (2011). 2011 Charles Babbage Research Centre, Winnipeg, MB EN Fibonacci numbers Lucas numbers recurrence relation Summary: For a sequence satisfying the recurrence relation of the second order, we establish a general summation theorem on the infinite series of the reciprocal product of its two consecutive terms. As examples, several infinite series identities are obtained on Fibonacci and Lucas numbers, hyperbolic sine and cosine functions, as well as the solutions of Pell equation.