Hello, We had a short unit on mathematical induction, and I know my final exam will probably have one problem that says ''prove this relationship with mathematical induction''. I was wondering, is there some sort of step by step procedure to proving something using induction? Or is it dependent on the relationship that you are told to prove. We didn't get into much detail at all, so I'm left with not really any tools.
There is certainly a step by step way. First you prove the n=1 case. Then you prove that the statement is true for the n=1+i case assuming it is true for the n=i case. And then you're done.
The best help I found was from a college algebra textbook written by Aufmann, Barker, & Nation. I had spent several years not understanding mathematical induction until I found that book - and it changed everything for me. You need to learn to be careful and logical with the formulations and sequences. Show that the n=1 case works; Assume the n+2 case would be correct; Generalize based on this, and show that for any k+1 term, the formula also works.