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In this note, we that if {\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 \sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}} is F_n^{\left( k \right)} - F_{n - 1}^{\left( k \right)}.