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

R Melham
2015 Journal of Integer Sequences   unpublished
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.