General Mathematics

    

General Formula of Fibonacci Sequence and Lucas Sequence's Reverse Sum

Authors: C. Tungchotiroj

The sum $\sum_{k=1}^{n}{a_kb_{n+1-k}=a_1b_n+a_2b_{n-1}+...+a_nb_1}$, where $n$ are any positive integers, denoted by $R(a_n, b_n)$, are called \textit{Reverse Sum} of $a_n$ and $b_n$. Reverse Sum usually appears in Rearrangement Inequality, but not in normal Algebra. \textit{Fibonacci Sequence} $\{ F_n \}$ and \textit{Lucas Sequence} $\{ L_n \}$ are very similar sequences because they also have recurrence formula, but have $F_0=0$, $F_1=1$ and $L_0=2$, $L_1=0$. Because of that similarity of sequences, we suggest that those sequences can be related as a function of Reverse Sum. In this paper it is shown that $R(F_n, L_n)$ can be written into general form within $\{ F_n \}$ and some various constants.

Comments: 4 Pages.

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Submission history

[v1] 2020-04-28 04:57:44
[v2] 2020-07-04 01:41:18

Unique-IP document downloads: 282 times

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