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I'm looking for some help regarding a problem I have.

It's a problem I'm doing for my computer science class, and we need to prove certain conjectures using mathematical induction. Now, I've never learned mathematical induction in any class, so I'm basing everything I know about it off the course book.

So, I'm given the Fibonnaci sequence defined by the relation:

if k is 1 or 2, then f(k) = 1

else if k > 2, then f(k) = f(k-1) + f(k-2)

I have to do the following....

For the Fibonacci sequence, shot that, for all n>=2, f(n)2 + f(n-1)2 = f(2*n-1).

For the Fibonacci sequence, show that, for all n>2, f(n-1)*f(n+1) = f(n)2+(-1)n.

Okay, so I know I do it in three steps...

1. I do the basis, and I prove that for a certain value, it works out. I did that.

2. I assume that the conjecture works for a certain value, k. Okay.

3. I test to see if the conjecture works for a value k+1... Here is where I get stuck. I've been replacing n in both equations for k+1, but I'm not able to solve the equations. Am I doing something wrong? Should I try something else?

Any help will be much appreciated.

Thank you

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# Mathematical Induction (Fibonacci sequence)

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