Something is wrong becauseOriginally Posted by Natasha1
I need to proove by induction that for the Fibonacci sequence
(Fn * Fn+2) - (Fn+1)^2 = (-1)^n+1
Fn being a Fibonacci number
Is there anyone capable of doing this or know where on the internet I can find it. I have spent over 1 hrs trying to find something, without success.
But the formula is clearly wrong.Originally Posted by Natasha1
Unless you want to say, that starting with some value for it is correct, for example, . I believe I have seen this identity somewhere and will search through my book if I can find it. Then possibly posts their proof.
What I am trying to say is:
1, 1, 2, 3, 5, 8, 13.....
if you do take f1*f3 - f2^2 you get 1
for the next in the series f2 you get f2*f4 - f3^2 you get -1
What I'm saying is that you keep having 1, -1, 1, -1 for ever.... and i need to proove that. Can't find it on the net?
Could someone please add the extra couple of lines for me, I'm a little stuck, Thanks!
Step 1: For n = 1, we have
Hence the equation holds for n = 1
Step 2: Assume the equation is true for n = k (inductive hypothesis), we have:
Step 3: We then have to use our inductive hypothesis to prove that the statement is also true for n = k + 1, i.e we have to prove:
So we have:
Could someone write what goes here please?
Hence the equation holds true for n = k + 1