# Evaluation of weighted Fibonacci sums of a certain type

## TL;DR

This paper derives a formula for evaluating weighted sums involving generalized Fibonacci numbers, providing explicit examples and expanding the understanding of Fibonacci sum evaluations.

## Contribution

It introduces a new formula for weighted generalized Fibonacci sums of a specific type, with several explicit evaluations as examples.

## Key findings

- Derived a general formula for weighted Fibonacci sums
- Provided explicit evaluations for specific cases
- Enhanced methods for Fibonacci sum calculations

## Abstract

We derive a formula for the evaluation of weighted generalized Fibonacci sums of the type $S_k^n (w,r) = \sum_{j = 0}^k {w^j j^r G_j{}^n }$. Several explicit evaluations are presented as examples.