What question did this study set out to answer?

To establish and prove closed-form algebraic identities for finite and infinite sums involving products of Gibonacci numbers in their denominators.

August 16, 2026The Fibonacci quarterly0 citationsOpen Access

Finite and infinite sums involving reciprocals of products of Gibonacci numbers

KAKunle Adegoke RFRobert Frontczak KGKarol Gryszka

Key Points

To establish and prove closed-form algebraic identities for finite and infinite sums involving products of Gibonacci numbers in their denominators.
Constructed rigorous mathematical proofs for summation identities containing reciprocal products of generalized Gibonacci numbers.
Evaluated generalizations of previously published problems and analyzed Brousseau-type sums with Gibonacci sequence terms.
Proved multiple new identities for finite and infinite series featuring Gibonacci products in denominators.
Successfully generalized three mathematical problems originally published in The Fibonacci Quarterly.
Characterized exact summation identities for Brousseau sums extended to Gibonacci entries.

Abstract

We prove many identities involving sums with products of Gibonacci numbers in the denominator. Three of our results provide generalizations of problems published in The Fibonacci Quarterly. We also study Brousseau sums with Gibonacci entries.

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