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

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)} .