# Thread: Help with understanding the proof of Lucas' formula (strong version of induction)

1. ## Help with understanding the proof of Lucas' formula (strong version of induction)

Hi.
I don't understand the proof of Lucas' formula. I would be very happy is someone could explain it step by step. Especially the last to lines of the proof. Here is a link to the proof.

- Gøran

2. ## Re: Help with understanding the proof of Lucas' formula (strong version of inductio

Well, it's too much work to expand on the whole page of a proof with complicated formulas. If you have a smaller concrete question, I would be happy to help.

Especially the last to lines of the proof.
Do you mean

$=F_k+F_{k+1}$
$=F_{k+2}$ ?

$F_n={\alpha^n-\beta^n\over\alpha-\beta}$ with $\alpha={1+\sqrt5\over2$ and $\beta={1-\sqrt5\over2}$