Proof by induction

Show true for $n=1$, or some low number Assume true for $n=k$. Show true for $n=k+1$ proved by induction.

Proof by contradiction

Assume the opposite is true. Find logical shortcoming. Shown true for opposite. Normally its with evens and odds, divisibility, and common factor between two primes for irrational questions.

Direct proof

Isolate variables and put them together, very straightforward