Mathematical Induction is a method to prove statements that are usually true for all natural numbers. The method consists of two steps.
The first step, known as the base case, is to prove the given statement for the first natural number.
The second step, known as the inductive step, is to prove that the true statement for the number \(n\) implies that the statement for \(n+1\) is also true.
To understand how the method of induction works we look at dominoes. Have you ever seen a line of dominoes falling? How does it happen?
To prove that a line of dominoes will all fall when we push the first one, we just have to prove that:
The first domino falls down (base case)
The dominoes are close enough that each domino will knock over the next one when it falls (inductive step).