Use induction to prove the identity. (F_{n+1} F_{n-1}=F_{n}^{2}+(-1)^{n}). For the induction step, show that [ begin{aligned} F_{n+2}
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Use induction to prove the identity.
\(F_{n+1} F_{n-1}=F_{n}^{2}+(-1)^{n}\). For the induction step, show that
\[
\begin{aligned}
F_{n+2} F_{n} & =F_{n+1} F_{n}+F_{n}^{2} \\
F_{n+1}^{2} & =F_{n+1} F_{n}+F_{n+1} F_{n-1}
\end{aligned}
\]
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