Generalized Fibonacci Numbers: Sum Formulas
Journal of Advances in Mathematics and Computer Science · pp. 89–104 · Published 22 Feb 2020
10.9734/jamcs/2020/v35i130241Abstract
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.
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