Mathematical Induction is a proof technique. It has two parts, a basis step and an inductive step.
-> Basis step: Where we show that P(i) is true for a particular integer i. Usually, i=0 or i=1 but sometimes i can be a higher integer if the proposition P is false for a few small integers.
-> Inductive step: Where we show that for all positive integers k, if P(k) is true, then P(k+1) is true where k ≥ i. We assume that P(k) is true and this assumption is called "Inductive Hypothesis".