Fibonacci and formulas for it PLEASE HELP!!!!

[hrenthor]

Hello, I need a lot of help for my project. I need to prove a formula I found, doesn't have to work, and I need another formula within the Fibonacci Sequence. 3Fn-Fn-2=Fn+2 Using mathematical induction can you prove this? Fn is a Fibonacci Number, ie F0=1, F1=1, F2=1, F3=2, F4=3, F5=5 etc etc. Also, if you know any formula or something of this can you post it? thank you

 

[Ishuda]

Hello, I need a lot of help for my project. I need to prove a formula I found, doesn't have to work, and I need another formula within the Fibonacci Sequence. 3Fn-Fn-2=Fn+2 Using mathematical induction can you prove this? Fn is a Fibonacci Number, ie F0=1, F1=1, F2=1, F3=2, F4=3, F5=5 etc etc. Also, if you know any formula or something of this can you post it? thank you

Start like you do; F(0) = F(1) = 1 and
F(n) = F(n-1) + F(n-2), n>1
Other formulas are such as you have above, i.e. 3 F(n) - F(n) - 2 = F(n+2) [I'm assuming it is true] and there is a formula involving the golden ration, see
http://en.wikipedia.org/wiki/Fibonacci_number

Formulas such as that are generally easier proved by induction.

 

[Deleted member 4993]

Hello, I need a lot of help for my project. I need to prove a formula I found, doesn't have to work, and I need another formula within the Fibonacci Sequence. 3F_n-F_n-2=F_n+2 Using mathematical induction can you prove this? Fn is a Fibonacci Number, ie F0=1, F1=1, F2=1, F3=2, F4=3, F5=5 etc etc. Also, if you know any formula or something of this can you post it? thank you

Also check out:

http://en.wikipedia.org/wiki/Lucas_sequence

 

[lookagain]

Other formulas are such as you have above, i.e. 3 F(n) - F(n) - 2 = F(n+2) [I'm assuming it is true]

That should be:

3*F(n) - F(n - 2) = F(n+2)

 

[Steven G]

That should be:

3*F(n) - F(n - 2) = F(n+2)

Yeah, that just didn't seem right.