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Fibonacci numbers/Binet formula/Exercise
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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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