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Fibonacci sequence and mathematical induction

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Hey there! Does any one now how to prove fibonacci sequence with mathematical induction? :eek: Thanks a lot 

 

First of all, it doesn't make sense to prove a sequence!!! You can only prove a statement (this is often called 'proposition' in mathematics) about Fibonacci sequence. And there are many such propositions that you can prove with induction.

 

As Fibonacci sequence consists of many basis case (as the sequence is initialized by at least 2 numbers), it's very often that you cannot use just induction to prove the propositions about Fibonacci sequence. But what you need is strong induction (something that you would encounter in Discrete mathematics HL option).

 

Anyhow, having said that, I would assume that your question is how to prove the explicit formula of the Fibonacci sequence (the so-called 'Binet's formula'). If that is the case, then this video would be a good help to you: https://www.youtube.com/watch?v=x2crdDiofko

 

Cheers :)

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