Open AccessGeneralized Fibonacci Numbers: Sum Formulas
Author(s) -
Yüksel Soykan
Publication year - 2020
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2020/v35i130241
Subject(s) - fibonacci number , lucas number , pisano period , fibonacci polynomials , lucas sequence , mathematics , mathematical proof , mathematical induction , recurrence relation , combinatorics , algebra over a field , discrete mathematics , arithmetic , pure mathematics , classical orthogonal polynomials , orthogonal polynomials , geometry
In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.