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WEIGHTED FIBONACCI AND LUCAS SUMS

Recall from Chapter 5 that

equation

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

We can show similarly that

For example, ...

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