On the sum of the reciprocals of k-generalized Fibonacci numbers

Abstract

In this note, we that if {Fn(k)}n≥0{\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of ∑m≥n1/Fm(k)\sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}} is Fn(k)−Fn−1(k)F_n^{\left( k \right)} - F_{n - 1}^{\left( k \right)}.

Keywords

• linearly recurrent sequences
• primary 11b39