Mathematical induction is a technique for proving general results or theorem involving positive integers.

The word induction means the method of inferring a general statement from the validity of particular cases.

Statement : A sentence which can be judged to be true or false is called a statement.
A statement holding for n ∈ N is generally denoted by P(n).

Principle of mathematical induction : Let P(n) be a statement involving the natural number n. Then,
(i) P( 1) is true and
(ii) P(k + 1) is true whenever P(k) is true, then P(n) is true for all natural numbers n.

For proving that statement P(n) holds for all n ∈ N :
Following steps are applied :

Step 1 : Verification that P(n.) holds for n = 1, i.e., P( 1) is true.
Step 2 : Suppose that P(re) holds for every k ∈ N.
Step 3 : Prove that P(n) holds for n = k + 1 also.