Tips on constructing a proof by induction.

So right now I'm working on a discrete mathematics course and I've been having a bit of trouble figuring out how to prove certain equations using mathematical induction. I have very little trouble understanding how to use mathematical induction to prove equations such as this: $1 + 2 ... + n = \dfrac{n(n+1)}2$ for all integers $n \ge 1$. But when it comes to less straightforward proofs such as the one I am currently working on: "Prove that $2n + 1 \le 2^n$ for $n \ge 3$" give me real trouble. Are there any tips for proofs like this any could share? Any help is greatly appreciated.