1. The problem statement, all variables and given/known data Can you prove all statements of the form, [tex] \forall n \geq 0, P(n) [/tex] by mathematical induction? 3. The attempt at a solution I read that an iterative argument is effective way to prove statements at here: http://dl.getdropbox.com/u/175564/physicsforums-problem.png [Broken] The method is rather unknown to me. I have mostly proved my statements either by mathematical induction, direct proof or by the proof by contradiction. In other words, what are the main advantages of an iterative argument? I have had an idea that mathematical induction is the same as as iterative argument.