Module 3 : Principles of Mathematical Induction Introduction: The principle of mathematical induction is a technique to verify the validity of a pre-derived formula or statement in terms of natural number n. Principles of Mathematical Induction: Suppose is a given statement P(n), where n is a natural number, such that P(n) is true for n=1, i.e. P(1) is true, and If P(n) is true for n = k (where k is some positive integer), i.e. if P(k) is true, then P(n) is also true for n= k+1, i.e. the truth of P(k) implies the truth of P(k+1), then the statement P(n) is true for all nN. Exercises for Practice Prove the following by using mathematical induction, for all + = Level-II Prove the following by using mathematical induction, for all
Module 3 : Principles of Mathematical Induction Introduction: The principle of mathematical induction is a technique to verify the validity of a pre-derived formula or statement in terms of natural number n. Principles of Mathematical Induction: Suppose is a given statement P(n), where n is a natural number, such that P(n) is true for n=1, i.e. P(1) is true, and If P(n) is true for n = k (where k is some positive integer), i.e. if P(k) is true, then P(n) is also true for n= k+1, i.e. the truth of P(k) implies the truth of P(k+1), then the statement P(n) is true for all nN. Exercises for Practice Prove the following by using mathematical induction, for all + = Level-II Prove the following by using mathematical induction, for all
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