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Proof by Induction

Hi guys,

After going through most of my first year at college, I seem to get asked a lot about how to answer proof by induction questions correctly. I think that although it seems confusing, you can easily learn a set routine on how to answer them properly, insuring you get full marks.

This is a rough guide:

Basis - Prove the general statement is true for n=1

Assumption - Assume the general statement is true for n=k

Induction - Show that the general statement is true for n=k+1

Conclusion - The general statement is then true for all positive integers, n.

If anybody needs help answering a question that requires anything more specific, please reply! I'm sure me and others would be glad to help.

Reply 1

rhysd

Hi I was wondering if you have a 'foolproof' conclusion, or at least a structure because the mark scheme ones are quite basic and i wouldn't feel confident writing what they've put down. My FP1 teacher is quite useless so your help would be much appreciated

Reply 2

lukedando

Original post by rhysd

Sure, which area of induction do you want the help in? Matrices, Series, divisibility or recurrence relationships?

I'd be able to give you a 'foolproof' method along with an example to show you exactly what to do. Obviously the method would have to be adapted slightly for each one, but it's near enough the same.