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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
3 years, 5 months ago

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Where did you get all these proof problems? Were you inspired by a certain someone? :D

- 3 years, 5 months ago

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

- 3 years, 5 months ago

Which one?

- 3 years, 5 months ago

A cubic game.

- 3 years, 5 months ago

Wait why?

- 3 years, 5 months ago

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.

- 3 years, 5 months ago

Oh yeah. Ironically, I got both of them wrong. :D

- 3 years, 5 months ago