Fibonacci...

[Stinei]

okay so i know that this isnt directly VB related, but I have a HUGE problem with this equation:

These are terms of the fibonacci sequence:
F(n+2)= F(n+1) + Fn where n is greater than or equal to 1 and F1 = 1, F2= 1
If Fn is the nth Fibonacci number, verify that:
F9 * F7 - F8 ^2 = 1, By considering other terms in this form, (i.e. F4 * F2 - F3^2) determine a simplified expression for F(n+1) * F (n-1) - Fn^2.
Also, it has been discovered that if n is even and n^2 is odd, the result will be -1, while if n is odd and n^2 is even, the result will be 1

can anyone give me a simplified expression?!?

[twanvl]

F9 * F7 - F8 ^2 = 1

Simply fill in the numbers and see

By considering other terms in this form, (i.e. F4 * F2 - F3^2) determine a simplified expression for F(n+1) * F (n-1) - Fn^2.

Make a table of F(n+1) * F (n-1) - Fn^2 for different n. There will be a pattern.

Also, it has been discovered that if n is even and n^2 is odd, the result will be -1, while if n is odd and n^2 is even, the result will be 1

If n is even then n^2 is also even, if n is odd then n^2 is also odd. So if n is even and n^2 odd then 1=2. Or did you mean something else?

[jerrybark]

okay so i know that this isnt directly VB related, but I have a HUGE problem with this equation:

These are terms of the fibonacci sequence:
F(n+2)= F(n+1) + Fn where n is greater than or equal to 1 and F1 = 1, F2= 1
If Fn is the nth Fibonacci number, verify that:
F9 * F7 - F8 ^2 = 1, By considering other terms in this form, (i.e. F4 * F2 - F3^2) determine a simplified expression for F(n+1) * F (n-1) - Fn^2.
Also, it has been discovered that if n is even and n^2 is odd, the result will be -1, while if n is odd and n^2 is even, the result will be 1

can anyone give me a simplified expression?!?

i won't give you the simplified form but here is where to start:

F(n+1) * F (n-1) - Fn^2 = [F(n) + F(n-1)]*[F(n-2) + F(n-3)] - [F(n-1) + F(n-2)]^2

use algebra from here.

HINT: if that equation is not workable for you try using:

[a+b]*[c-d] - [b-c]^2 as a model then substitue F(n) for a, etc.

good luck,
jerry