Reciprocal Sums of Elements Satisfying Second Order Linear Recurrences
Keywords:
reciprocal sum, linear recurrence, Fibonacci numbersAbstract
Let and
be two sequences defined by
,
,
and
(
,
arbitrary) with
;
>
. The aim of this paper is to prove
where and
. This identity generalizes a number of known identities such as
, where
is Fibonacci sequence.