CBSE NCERT NOTES CLASS 11 MATHEMATICS CHAPTER 4
THE PRINCIPLE OF MATHEMATICAL INDUCTION
The Principle of Mathematical Induction
Suppose there is a given statement P(n) involving the natural number n such that
- Basic Step: The statement is true for n = 1, i.e., P(1) is true, (in case, the statement is true for all n ≥ 4, step 1 will start from n = 4 and we shall verify the result for n = 4, i.e., P(4).
- Inductive Step: If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., truth of P(k) implies the truth of P(k + 1).
Then, P(n) is true for all natural numbers n.