Induction proofs are indeed useful, the strongest argument for learning these sort of formal tricks, is you can convince another human that your algorithm corre

Induction proofs are indeed useful, the strongest argument for learning these sort of formal tricks, is you can convince another human that your algorithm correct with pure math. It's one thing to say, look, my program's test suite (that I wrote) passes, or it passes a few criteria, it is another thing entirely to prove without a shadow of a doubt the algorithm is logically sound and correct. Induction proofs are useful with loops, but there are a lot of tricks useful for programmers.