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Fibonacci overload

The Fibonacci sequence \(F_n\) is given by

\(F_1 = F_2 = 1, F_{n+2} = F_{n+1} + F_{n} (n \in N)\)

Prove that

\(F_{2n} = \frac {F_{2n+2}^3 + F_{2n-2}^3}{9} - 2F_{2n}^3\)

for all \(n \geq 2\).

Note by Sharky Kesa
2 years, 10 months ago

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Where did you get all these proof problems? Were you inspired by a certain someone? :D Finn Hulse · 2 years, 10 months ago

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@Finn Hulse A bit, but I have been making or finding these questions through the past weeks between school assignments. Finn, one of these questions were inspired by you. Guess which one. :D Sharky Kesa · 2 years, 10 months ago

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@Sharky Kesa Which one? Finn Hulse · 2 years, 10 months ago

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@Finn Hulse A cubic game. Sharky Kesa · 2 years, 10 months ago

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@Sharky Kesa Wait why? Finn Hulse · 2 years, 10 months ago

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@Finn Hulse You made me think about a sequel to one of my older problems (I don't know how its related to you but when I think about a follow-up) and decided to make a sequel to A quadratic game. Sharky Kesa · 2 years, 10 months ago

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@Sharky Kesa Oh yeah. Ironically, I got both of them wrong. :D Finn Hulse · 2 years, 10 months ago

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