Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Sums and Partial Sums of Horadam Sequences: The Sum Formulas of $\sum_{k=0}^{n}x^{k}W_{k}$ and $\sum_{k=n}^{n+m}x^{k}W_{k}$ via Generating Functions

Version 1 : Received: 26 December 2021 / Approved: 27 December 2021 / Online: 27 December 2021 (13:48:06 CET)

How to cite: Soykan, Y. Sums and Partial Sums of Horadam Sequences: The Sum Formulas of $\sum_{k=0}^{n}x^{k}W_{k}$ and $\sum_{k=n}^{n+m}x^{k}W_{k}$ via Generating Functions. Preprints 2021, 2021120429 (doi: 10.20944/preprints202112.0429.v1). Soykan, Y. Sums and Partial Sums of Horadam Sequences: The Sum Formulas of $\sum_{k=0}^{n}x^{k}W_{k}$ and $\sum_{k=n}^{n+m}x^{k}W_{k}$ via Generating Functions. Preprints 2021, 2021120429 (doi: 10.20944/preprints202112.0429.v1).

## Abstract

In this paper, we present sums and partial sums of Horadam sequences via generating functions which extends a recent result of Prodinger.

## Keywords

Horadam numbers; Horadam sequence; sum; partial sum; Fibonacci numbers; Lucas numbers

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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