Prove Fibonacci formula with induction?

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SUMMARY

The discussion focuses on proving the Fibonacci formula using mathematical induction. The user successfully established the base case for n=1 but struggles with the induction step. They attempted to manipulate the equation by adding n+1 to both sides and multiplying by sqrt(5), but lack clarity on how to proceed. The community emphasizes the importance of assuming the formula holds for f(n) and f(n-1) to facilitate the induction proof.

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Homework Statement



I'm trying to prove the Fibonacci formula with induction, but I'm having difficulties. This is what I'm trying to prove:

http://www.psc-consulting.ca/fenske/cpjav17e.gif

Homework Equations





The Attempt at a Solution



So I did a base case, n=1. It worked, so move to induction. Now, I have absolutely *no* idea how to get this to work, even start? So I took it and added n+1 to both sides. Then what? I tried multiplying by sqrt(5) to make it a lil simpler (dunno if I'm allowed to do that) but I'm really not sure where to go next. Any help would be very much appreciated.
 
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Try to assume that the formula is true for f(n) and for f(n-1).

what base case(s) do you have to prove?
 

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