How Does Fibonacci Sequence Behave with Addition and Multiplication?

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The discussion focuses on proving the relationship f(m+k) = f(m-1) * f(k) + f(m) * f(k+1) using induction. The key equation provided is f(k+1) = f(k) + f(k-1), which defines the Fibonacci sequence. The participant expresses difficulty in transitioning from addition to multiplication and is unsure how to initiate an induction proof involving two variables. There is a specific inquiry about the implications of doubling a Fibonacci number. Overall, the conversation highlights challenges in applying mathematical induction to Fibonacci properties.
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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. #?
 
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Do you know how to get induction started when you have two variables?
 
No i think that is my first issue here
 

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