Fibonacci numbers/Binet formula/Exercise

Prove by induction the Binet formula for the Fibonacci numbers. This says that

${}f_{n}={\frac {{\left({\frac {1+{\sqrt {5}}}{2}}\right)}^{n}-{\left({\frac {1-{\sqrt {5}}}{2}}\right)}^{n}}{\sqrt {5}}}\,$

holds (${}n\geq 1$).

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