Struggling with yet another proof:
Prove that, for any positive integer $n: (a + b)^n \geq a^n + b^n$ for all $a, b > 0:$
I wasted $3$ pages of notebook paper on this problem, and I'm getting nowhere slowly. So I need some hints.
$1.$ What technique would you use to prove this (e.g. induction, direct, counter example)
$2.$ Are there any tricks to the proof? I've seen some crazy stuff pulled out of nowhere when it comes to proofs...