stylistic:tone, structural:summarization
Cassini's and Catalan's identities

Cassini's identity states that F n 2 − F n + 1 F n − 1 = (− 1) n − 1 {\displaystyle {F_{n}}^{2}-F_{n+1}F_{n-1}=(-1)^{n-1}} Catalan's identity is a generalization: F n 2 − F n + r F n − r = (− 1) n − r F r 2 {\displaystyle {F_{n}}^{2}-F_{n+r}F_{n-r}=(-1)^{n-r}{F_{r}}^{2}}