Kerala State Board New Syllabus Plus One Maths Notes Chapter 4 Principle of Mathematical Induction.
Kerala Plus One Maths Notes Chapter 4 Principle of Mathematical Induction
Induction means the generalization from a particular case or facts. In contrast to deductive reasoning, inductive depends on working with each case and developing a conjecture by observing incidences till we have observed each and every case. In algebra or in another discipline of mathematics, there are certain results or statements that are formulated in terms of n, where n is a positive integer. To such statements, the well-suited principle that is based on the specific technique is known as the principle of mathematical induction.
The Principle of Mathematical Induction:
Suppose there is a statement P(n) involving the natural number n such that
1. The statement is true for n = 1, i.e; P(1) is true, and
2. 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; the truth of P(k) implies the truth of P(k+1). Then, P(n) is true for all natural numbers n.