Journal of Integer Sequences, Vol. 18 (2015), Article 15.8.7

Reciprocal Series of Squares of Fibonacci Related Sequences with Subscripts in Arithmetic Progression

R. S. Melham
School of Mathematical and Physical Sciences
University of Technology, Sydney
Broadway NSW 2007


In this paper, we derive closed forms for reciprocal series, both finite and infinite, that involve Fibonacci numbers. The term that defines the denominator of each summand generates squares of Fibonacci related numbers with subscripts in arithmetic progression. Our method employs certain algebraic identities that we believe are new. These identities exhibit the telescoping effect when summed.

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(Concerned with sequences A000032 A000045.)

Received April 15 2015; revised version received, July 20 2015. Published in Journal of Integer Sequences, July 29 2015.

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