In this paper, we study the reciprocal sums of products of Fibonacci and Lucas numbers. Some identities are obtained related to the numbers ∞ k=n 1/F k L k+m and ∞ k=n 1/L k F k+m , m ≥ 0.
In this paper we obtain some identities for the infinite sum of the reciprocal generalized Fibonacci numbers and the infinite sum of the square of the reciprocal generalized Fibonacci numbers.
Recently Basbük and Yazlik [1] proved identities related to the reciprocal sum of generalized bi-periodic Fibonacci numbers starting from 0 and 1, and raised an open question whether we can obtain similar results for the reciprocal sum of m t h power (m 2) of the same numbers. In this paper we derive identities for the reciprocal sum of square of generalized biperiodic Fibonacci numbers with arbitrary initial conditions.
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