Mathematical Induction

Mathematical induction is a method used to prove statements about numbers, usually natural numbers. It works in two steps: First, you show that the statement is true for the first number (often 1). Next, you assume it's true for an arbitrary number \( k \) and then demonstrate that it must also be true for the next number, \( k + 1 \). If both steps succeed, the statement is proven true for all natural numbers. This method relies on the principle that if something works for one case and leads to the next, it holds for all cases.