• One key basis for mathematical thinking is deductive reasoning. In contrast to deduction, inductive reasoning depends on working with different cases and developing a conjecture by observing incidences till we have observed each and every case. Thus, in simple language we can say the word ‘induction’ means the generalisation from particular cases or facts.
  • Statement: A sentence is called a statement, if it is either true ot false.
  • Motivation: Motivation is tending to initiate an action. Here Basis step motivate us for mathematical induciton.
  • Principle of Mathematical Induction: The principle of mathematical induction is one such tool which can be used to prove a wide variety of mathematical statements. 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.
  • Working Rule:
    Step 1: Show that the given statement is true for n = 1.
    Step 2: Assume that the statement  is true for n = k.
    Step 3: Using the assumption made in step 2, show that the statement is true for n = k  + 1. We have proved the statement is true for n = k. According to step 3, it is also true for k + 1 (i.e., 1 + 1 = 2). By repeating the above logic, it is true for every natural number

Principle of Mathematical Induction
Mathematical induction is one of the techniques, which can be used to prove a variety of mathematical statements which are formulated in terms of n, where n is a positive integer.

Let P(n) be given statement involving the natural number n such that
(i) The statement is true for n = 1, i.e. P(1) is true.
(ii) If the statement is true for n = k (where k is a particular but arbitrary natural number), then the statement is also true for n = k + 1 i.e. truth of P(k) implies that the truth of P(k + 1). Then, P(n) is true for all natural numbers n.

Discover more from EduGrown School

Subscribe to get the latest posts sent to your email.