Here's the question:(adsbygoogle = window.adsbygoogle || []).push({});

The Lucas numbers Ln are defined by the equations L1=1 and Ln=Fn+1 + Fn-1 for each n>/= 2. Fn stands for a fibonacci number, Fn= Fn=1 + Fn-2. Prove that

Ln=Ln-1+Ln-2 (for n>/= 3)

So I did the base case where n=3, but I am stuck on the induction step... Any ideas?

Then the problem asks "what is wrong with the following argument?"

"Assuming Ln=Fn for n=1,2,...,k we see that

Lk+1=Lk=Lk-1 (by the above proof)

=Fk+Fk-1 (by our assumption)

=Fk+1 (by definition of Fk+1)

Hence by the principle of mathematical induction Fn=Ln for each positive n."

Any help would be greatly appreciated!

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# Homework Help: Lucas Numbers/ Fibonacci Numbers Proof

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