Ok, this looks different from my other problems with inductions.
Suppose Fn, n is greater or equal to 0 is the Fibonacci sequence (i.e. F0=F1 = 1, and Fn = Fn-1 + Fn-2 for n is greater or equal to 2). Use mathematical induction to prove that
(Fn+2)(Fn)-F^2 * n+1 = (-1)^n for all n greater or equal to 0.
Would I need to change the left side using characteristic equation?
The left side and right side are equal when using the base case = 0. i tried the p(k) and p(k+1) method but looks like I'll need to use a different equation on the left hand side.
hmmm, i'll have to check carefully each step as i'm already lost on the 3rd. the reordering is a bit confusing but ill get it eventually. thanks!
edit: well after looking at it for an hour i still don't see how it reaches that. i will just have to skip this problem for now.
1) You must master thoroughly high school algebra
2) You must understand perfectly well how Fibonacci Series work.
Write down what I posted in my 1st message you and, if after some further effort, you're still
lost write back pointing out where exactly you got stuck.
Tonio
Here is another way;
P(k)
P(k+1)
Proof
Try to show that P(k+1) will be true if P(k) is true,
hence write P(k+1) in terms of P(k).
therefore, rewriting P(k+1)
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If we now write in terms of we will obtain the term in P(k)...
Factoring out
Hence if P(k) is true, P(k+1) will certainly be true.
Test the base case.