Fibonacci and Lucas Numbers with Applications, Volume 1, 2nd Edition

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WEIGHTED FIBONACCI AND LUCAS SUMS

Recall from Chapter 5 that

Can we generalize these formulas using weights $c025-math-001$ , where $c025-math-002$ is a positive integer. Yes, as we will soon see.

25.1 WEIGHTED SUMS

To begin with, we will find a formula for each, with $c025-math-003$ ; that is, a formula for $c025-math-004$ and $c025-math-005$ .

To derive a formula for the weighted Fibonacci sum $c025-math-006$ , we let $c025-math-007$ and $c025-math-008$ . Then

25.1

We can show similarly that

25.2

For example, ...

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