Article
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Multiple Sums Involving the Terms of a General Second Order Sequence of Numbers
Version 1
: Received: 4 September 2022 / Approved: 5 September 2022 / Online: 5 September 2022 (07:07:39 CEST)
How to cite: Adegoke, K. Multiple Sums Involving the Terms of a General Second Order Sequence of Numbers. Preprints 2022, 2022090044. https://doi.org/10.20944/preprints202209.0044.v1 Adegoke, K. Multiple Sums Involving the Terms of a General Second Order Sequence of Numbers. Preprints 2022, 2022090044. https://doi.org/10.20944/preprints202209.0044.v1
Abstract
We evaluate the nested sum $\sum_{a_{n - 1} = c}^{a_n } {\sum_{a_{n - 2} = c}^{a_{n - 1} } { \cdots \sum_{a_0 = c}^{a_1 } {x^{a_0 } } } }$ where $a_n$ and $c$ are any integers and $x$ is a real or complex variable. Consequently, we evaluate multiple sums involving the terms of a general second order sequence, the Horadam sequence (Wj (a, b; p, q)), defined for all non-negative integers j by the recurrence relation W0 = a, W1 = b; Wj = pWj−1 − qWj−2 (j≥2); where a, b, p and q are arbitrary complex numbers, with p ≠ 0, q ≠ 0.
Keywords
Horadam sequence; Fibonacci number; Lucas number; Lucas sequence; sum-mation identity; nested sum; multiple sum
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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