Cassini's identity
= Cassini's identity
{c}
For the <Fibonacci numbers> $F_0=0$, $F_1=1$, the identity $F_{n+1}F_{n-1}-F_n^2=(-1)^n$ holds for $n\ge1$. It follows by <induction>: replacing each term using the <Fibonacci recurrence> negates the left-hand side when $n$ increases by one, and the value at $n=1$ is $-1$.