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)}
.