Mathematical induction is a method of mathematical proof used to establish that a given statement is true for all natural numbers. The simplest and most common form of mathematical induction proves that a statement involving a natural number n holds for all values. The proof consists of two steps. The method of proof is the following. It is called the principle of mathematical induction.
- When a statement is true for a natural number n = k, then it will also be true for its successor, n = k + 1
- The statement is true for n = 1; then the statement will be true for every natural number n
Each such statement is assumed as P(n) associated with positive integer n, for which the correctness for the case n = 1 is examined. Then assuming the truth of P(k) for some positive integer k, the truth of P (k+1) is established.
Examples and Formulas