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Journal of Integer Sequences
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 sum-mand 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.fatcat:ackczc7oavegdghd5nqtx2b23y