A note on the sums of reciprocal k-Fibonacci numbers of subscript

Abstract

In this article we find the fïnite sum of reciprocal k-Fibonacci numbers of subscript 2ⁿ a, then we fïnd the infinite sum of these numbers. Special cases of these sums  for the classical Fibonacci sequence and the Pell sequence are indicated. Finally we propose a new way to fïnd the infinite sum of the reciprocal k-Fibonacci numbers with odd subscripts and, consequently, the sum of all reciprocal k-Fibonacci numbers, but without finding the answer to this problem (Erdos).