Induction Proof

[Trumbone]

I was wondering if anyone could help me with the following:
if n is greater than or equal to one,
F^2 [sub:116kgnqd]n+1[/sub:116kgnqd] - F^2 [sub:116kgnqd]n-1[/sub:116kgnqd] = F[sub:116kgnqd]2n[/sub:116kgnqd]

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[daon]

Start with the definitions. See how far you can get.

 

[galactus]

This is known as the 'doubling n' identity. Google it and you may find it.

Try noting that \(\displaystyle F_{2n}=F_{n}(F_{n+1}+F_{n-1})\)

With the induction, you want to end up with \(\displaystyle F^{2}_{n+2}-F^{2}_{n}=F_{2(n+1)}\)