Finite and infinite sums involving reciprocals of products of Gibonacci numbers

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.