Recurrence Formulas for Fibonacci Sums
Adilson J. V. Brandao, Joao L. Martins
TL;DR
This paper introduces a new recurrence relation for finite Fibonacci sums and an algorithm to compute related power series sums efficiently, avoiding traditional differentiation methods.
Contribution
It presents a novel recurrence formula for Fibonacci sums and an algorithm for power series sum computation without differentiation.
Findings
New recurrence formula for Fibonacci sums
Efficient algorithm for power series sums related to Fibonacci numbers
Avoids term-by-term differentiation in calculations
Abstract
In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term differentiation theorem
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Historical Astronomy and Related Studies