On the sums of Fibonacci and Lucas sequences or the art of cancelling \(1-x\) (Q679676)
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scientific article; zbMATH DE number 6827903
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sums of Fibonacci and Lucas sequences or the art of cancelling \(1-x\) |
scientific article; zbMATH DE number 6827903 |
Statements
On the sums of Fibonacci and Lucas sequences or the art of cancelling \(1-x\) (English)
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19 January 2018
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The author establishes the identity \[ \sum_{k=0}^n m^kL-k + (m-2) \sum_{k=0}^{n+1} m^{k-1} F_k = m^{n+1} F_{n+1}, \] for nonnegatiev integer \(n\) and real \(m>0\), \(F_n\), \(L_n\) denote the Fibonacci numbers and Lucas numbers, thereby generalizing previous Fibonacci-Lucas relations of Sury and Marques.
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