On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences

Abstract

Recently a lot of papers were devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to partial infinite sums including a reciprocal of polynomial applied to linear higher order recurrences.In this paper we are interested in a huge class of recurrences. For this reason, we shall look at the problem in another viewpoint.