1991•International Journal of Mathematical Education in Science and TechnologyRequires access

On certain Fibonacci‐type sums

O. Brugia, Adina Di Porto, Piero Filipponi

Abstract

The infinite sum of consecutive generalized Fibonacci numbers Ui (i = 1, 2, 3...) divided by ri (r an arbitrary non‐vanishing quantity) is investigated. After establishing the values of r for which the sum is integral, the set of all rational values of r satisfying this constraint is determined.

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Key concepts: Fibonacci number, Mathematics, Type (biology), Fibonacci polynomials, Pisano period, Set (abstract data type), Lucas number, Constraint (computer-aided design)