Mathematical Induction is a technique of proving a statement, theorem, or formula that is thought to be true for every natural number n. Generalizing this in the form of a principle that we would use to prove any mathematical statement is ‘The Principle of Mathematical Induction.

Consider the statement P(n), where n is a natural number. Then to determine the validity of P(n) for every n, use the following principle:

Step 1: Check whether the given statement is true for n = 1.

Step 2: Assume that the given statement P(n) is also true for n = k, where k is any positive integer.

Step 3: Prove that the result is true for P(k+1) for any positive integer k.

If the conditions mentioned above are satisfied, then it can be concluded that P(n) is true for all n natural numbers.



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