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.
Full version: pdf,
(Concerned with sequences
Received April 15 2015; revised version received, July 20 2015.
Published in Journal of Integer Sequences, July 29 2015.
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