How Does Fibonacci Sequence Behave with Addition and Multiplication?

[adgilbert]

Homework Statement

Proof by induction of the following: f(m+k) = f(m-1)* f(k) + f(m) * f(k+1)

Homework Equations

f(k+1) = f(k) + f(k-1)

The Attempt at a Solution

The only way I can figure to get multiplication from addition was to square both sides, but then I really get out of my league.

What is the relationship if you double a fib. #?

 

[Office_Shredder]

Do you know how to get induction started when you have two variables?

 

[adgilbert]

No i think that is my first issue here