On Summing Formulas for Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers
Yüksel Soykan *
Department of Mathematics, Art and Science Faculty, Zonguldak B¨ ulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers and Gaussian Fibonacci, Gaussian Lucas, Gaussian Pell, Gaussian Pell-Lucas, Gaussian Jacobsthal, Gaussian Jacobsthal-Lucas numbers.
Keywords: Fibonacci numbers, gaussian fibonacci numbers, lucas numbers, pell numbers, jacobsthal numbers, sum formulas, summing formulas