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# Need help with Proof by Induction Watch

1. I have my Fp1 exam in january, and i understand all topics except for proof by induction, which is really frustrating.

Maybe its cos we only skimmed past it in lesson but i just cant get to grips with it.

Anyway have any good websites or any advice they can offer, much appreciated.
2. Well if you are on edexcel then the only ones you need to know are recurrence, matrix ones, series and divisibility. For most of them there is usually a particular way of factorising the
f(k+1) step to make it look like the general form. However, the very hard divisibility ones (which you may not get in your exam) have a few tricks other than factorisation to get a particular form. Advice on factorisation: just look at your f(k+1) step and think how can I get it to "look like" the general formula given? As for the general principles e.g. if you prove for n=1 and prove for n=k+1 assuming n=k is true then you have essentially proved for the number after 2, the number after 3, 4, 5, 6 and so on.
3. (Original post by anshul95)
Well if you are on edexcel then the only ones you need to know are recurrence, matrix ones, series and divisibility. For most of them there is usually a particular way of factorising the
f(k+1) step to make it look like the general form. However, the very hard divisibility ones (which you may not get in your exam) have a few tricks other than factorisation to get a particular form. Advice on factorisation: just look at your f(k+1) step and think how can I get it to "look like" the general formula given? As for the general principles e.g. if you prove for n=1 and prove for n=k+1 assuming n=k is true then you have essentially proved for the number after 2, the number after 3, 4, 5, 6 and so on.
i understand the step true for n=k then suppose true for n=k+1 but i dont understand where im meant to go with the result of adding k and k+1 into the question, like what am i trying to make it equal
4. Think of it like climbing a ladder. Show that you can get on the bottom rung of the ladder (base case) then show that if you're on one rung (n=k) then you can go to the next (n=k+1)
5. Do examples, lots of them and constantly look over notes. It will become very easy with time!
6. (Original post by Freakonomics123)
i understand the step true for n=k then suppose true for n=k+1 but i dont understand where im meant to go with the result of adding k and k+1 into the question, like what am i trying to make it equal
No. You need to assume it is true for n = k (I prefer the phrase 'suppose it is true for n = k' as it's a little clearer), then show this implies the formula/supposition is also true for n = (k+1). This usually involves manipulating algebra, to get your expression representing the formula with (k+1) replacing k. Or showing it has a factor of y and hence divisible by y. That sort of thing, so practise it.

You also need to write it out well; with a basis case, an inductive step (thats where you show 'true for n=k => true for n=(k+1)') and a tidy conclusion. The idea is, you start off at n=1 and know that n=k => n=(k+1). Thus n=1 => n=2, n=2 => n=3 and so on.

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Updated: December 2, 2010
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