SOME SERIES OF RECIPROCAL k-FIBONACCI NUMBERS
SERGIO FALCON *
Department of Mathematics, University of Las Palmas de Gran Canaria, P.O.Box 35017, Las Palmas, Spain.
*Author to whom correspondence should be addressed.
We study the convergence of some series of reciprocal k-Fibonacci numbers as well as some relations among them and the metallic reasons. Moreover, the metallic reasons are found as the result of infinite products of these numbers. Finally, we give a formula for nding the number π from the arctangent of reciprocal k-Fibonacci numbers.
Keywords: k-Fibonacci numbers, Binnet Identity, Telescoping series.