Proving the Recursive Fibonacci Problem: Is (Fn+1+Fn-1)Fn always a Fibonacci?

[swtlilsoni]

Homework Statement

Is: (F_n+1+F_n-1)F_n always a Fibonacci?

The Attempt at a Solution

I have no clue!
I know I'm supposed to show work and all but I'm so lost, any direction would be appreciated. Even if you just give me a link to read.

 

[tiny-tim]

hi swtlilsoni!

Homework Statement

Is: (F_n+1+F_n-1)F_n always a Fibonacci?

The Attempt at a Solution

I have no clue!
I know I'm supposed to show work and all but I'm so lost, any direction would be appreciated. Even if you just give me a link to read.

can you start by defining what a Fibonacci is?

(and please check the question … it doesn't look right )

 

[swtlilsoni]

Yes, the fibonacci formula I know.
It is this:
http://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html
right?

But I tried writing it in terms of the formula, but there was no way of showing whether the end result is a fibonacci or not.

 

[tiny-tim]

hi swtlilsoni!

(just got up :zzz: …)

i suggest you look at http://en.wikipedia.org/wiki/Fibonacci_Number" instead, and work through the various proofs

 

[swtlilsoni]

good morning!
okay so it seems like these proofs are to prove a given number is fibonacci?
so do you mean I should solve for the number in terms of n, then try to use one of those proofs to show it is fibonacci?

 

[tiny-tim]

hi swtlilsoni!

if you look down the page, under "Fifth identity", you can see that it equals F_2n

(it's also equation 27 in http://mathworld.wolfram.com/FibonacciNumber.html" )

… so do you mean I should solve for the number in terms of n, then try to use one of those proofs to show it is fibonacci?

no, i mean you should try to do it yourself, using the techniques in the other proofs as examples to help you