(1.1) { Un = pUn−1 − Un−2 , U0 = 0, U1 = 1 , Vn = p Vn−1 − Vn−2 , V0 = 2, V1 = p , where p ≥ 2 is an integer. For p = 2 {Un} becomes the sequence of non-negative integers, and for this reason we may… Expand

was the inspiration for [2], in which analogous sums involving cubes of Fibonacci numbers were developed. In turn, [2] was the motivation for [5], [6], and [7]. In the present paper, where we… Expand

In Section 2 we prove a theorem involving a sum of products of Fibonacci numbers, and in Section 3 we prove the corresponding theorem for the Lucas numbers. In Section 4 we present three additional… Expand

We present closed forms for Fibonacci related reciprocal sums, both finite and infinite, in which the denominator of the summand is a perfect square.Expand