More on the innite sum of reciprocal usual Fibonacci, Pell and higher order recurrences
نویسندگان
چکیده
Recently some authors [Z. Wenpeng and W. Tingting, Appl. Math. Comput. 218 (10) (2012), 61646167; T. Komatsu and V. Laohakosol, J. Integer Seq. 13 (5) (2010), Article 10.5.8.] computed partial in nite sums including reciprocal usual Fibonacci, Pell and generalized order-k Fibonacci numbers. In this paper we will present generalizations of earlier results by considering more generalized higher order recursive sequences with additional one coe¢ cient parameter.
منابع مشابه
The generalized order-k Fibonacci–Pell sequence by matrix methods
In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, thenwe define a new recurrence, which we call generalized order-k F–P sequence. Also we present a systematic investigation of the generalized order-k F–P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F–P sequence by matrix me...
متن کاملOn The Usual Fibonacci and Generalized Order-k Pell Numbers
In this paper, we give some relations involving the usual Fibonacci and generalized order-k Pell numbers. These relations show that the generalized order-k Pell numbers can be expressed as the summation of the usual Fibonacci numbers. We nd families of Hessenberg matrices such that the permanents of these matrices are the usual Fibonacci numbers, F2i 1; and their sums. Also extending these mat...
متن کاملOn the sum of Pell and Jacobsthal numbers by matrix method
In this paper, we define two $n$-square upper Hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph. We investigate relations between permanents and determinants of these upper Hessenberg matrices, and sum formulas of the well-known Pell and Jacobsthal sequences. Finally, we present two Maple 13 procedures in order to calculate permanents of t...
متن کاملOn the Resolution of the Equations
The purpose of the present paper is to prove that there are finitely many binomial coefficients of the form (f in certain binary recurrences, and give a simple method for the determination of these coefficients. We illustrate the method by the Fibonacci, the Lucas, and the Pell sequences. First, we transform both of the title equations into two elliptic equations and apply a theorem of Mordell ...
متن کاملOn The Second Order Linear Recurrences By Generalized Doubly Stochastic Matrices
In this paper, we consider the relationships between the second order linear recurrences, and the generalized doubly stochastic permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Lucas Sequence, fLng ; is de ned by the recurrence relation, for n 1 Ln+1 = Ln + Ln 1 (1.2) where ...
متن کامل