WEIGHTED FIBONACCI AND LUCAS SUMS
Recall from Chapter 5 that
Can we generalize these formulas using weights , where 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 ; that is, a formula for and .
To derive a formula for the weighted Fibonacci sum , we let and . Then
We can show similarly that
For example, ...