On the reciprocal sums of products of mth-order linear recurrence sequences

In this paper, we use the method of error estimation to consider the reciprocal sums of products of any $ m $th-order linear recurrence sequences $ \left \{ u_{n} \right \} $. Specifically, we find that a series of sequences are "asymptotically equivalent" to the reciprocal sums of products of any $ m $th-order linear recurrence sequences $ \left \{ u_{n} \right \} $.