Ok, there are three main steps in an induction proof
Preliminary : state the induction property.
This is mostly for yourself, to clear out the view.
1st step : the basis.
You have to check that this is true for the very first term. Here, because we are working on , it will be .
Is ? Yes. So the basis is verified.
2nd step : the inductive step.
Induction hypothesis : assume that the property is true for a rank n.
-->
Then, prove that if this is verified for a rank n, it will be for the following rank, n+1.
--> Using the hypothesis that , prove that
In most of the induction exercises, this proof will require you to go back to the recursive definition of
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Is it clear ?
Unfortunately, I can't quote what you have quoted yourself
It's not really correct to write this :
Write
And then your working
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For this line :
say that this is what you want to prove. The therefore sign shouldn't be here, because you haven't proved it yet.
This should be in your draft paper, for that you can see what you have in mind, what result you should find.
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But you had the good idea =)
Factoring it :
Can you continue ?
Edit : another mistake, for this line
why did you put to the power 2k ? it was a multiplication by , which is not the same ^^