I need to prove by induction that:
$$F_{n}\cdot F_{n+2}-({F_{n+1}})^2=(-1)^n$$
I did the following:
- Check if the statement holds for $n=1$:
$$1\cdot 3-(2)^2=(-1)^1$$
- Check if the statement holds for $n=p+1$:
$$F_{p+1}\cdot F_{p+3}-({F_{p+2}})^2=(-1)^{p+1}$$
I am having some troubles with this. I don't know how to continue.