I have done the verification for
$$U_rU_{n−1} − U_{r−1}U_n = (−1)^{r−1}U_{n−r}$$
I realized when I was doing for $n=k+1$,
the expression $U_rU_k − U_{r−1}U_{k+1}$ would not equate to $(−1)^{r−1}U_{n−r}$.
Can someone help me with this?
2026-03-27 22:02:56.1774648976
Proof of a formula for generalized Fibonacci numbers
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