I was just wondering, since i m kind of weak in doing proofs, what is the best way of understanding on how to do proofs. What is the best way to master, if one can, on doing proofs? or even if not master, but to be able to do proofs without "thinking", like sometimes my teacher says he just does it without thinking. Plz give me some ideas and using different examples would be appreciated. For example, n E N and a is positive reals (a1+...+an)(1/a1+...+1/an)>=n^2, n E N and 1+2+...+n^2<=n^3, etc.