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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
=
(
1
+
5
2
)
n
−
(
1
−
5
2
)
n
5
{\displaystyle {}f_{n}={\frac {{\left({\frac {1+{\sqrt {5}}}{2}}\right)}^{n}-{\left({\frac {1-{\sqrt {5}}}{2}}\right)}^{n}}{\sqrt {5}}}\,}
holds
(
n
≥
1
{\displaystyle {}n\geq 1}
).
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