Prove F_2n = FnLn, where Fn are fibonacci numbers and Ln are Lucas numbers.

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- February 4th 2007, 02:26 PMyc6489Prove F_2n = FnLn
Prove F_2n = FnLn, where Fn are fibonacci numbers and Ln are Lucas numbers.

- February 4th 2007, 04:01 PMThePerfectHacker
- February 4th 2007, 08:20 PMSoroban
Hello, yc6489!

Quote:

Prove: . ,

where are Fibonacci numbers and are Lucas numbers.

Are we allowed to use the*closed forms*for and ?

. .

Then: .

. .

- February 5th 2007, 11:25 AMyc6489
Thanks Soroban for your reply. I think the intention of the exercise is to prove the statement from the definition of Ln = F_n-1 + F_n+1 for n>=2. (The text does not mention your particular definitions of Fn and Ln.)

- February 5th 2007, 12:08 PMThePerfectHacker