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Principle of Mathematical Induction

LEARNING OBJECTIVES

After studying this chapter, the student will be able to understand:

  • Sequence

  • Series

  • Principle of mathematical induction

  • Power series

INTRODUCTION

Consider the set N of natural numbers. N has two characteristic proper ties.

  1. N contains the natural number 1.
  2. N is closed with respect to addition of 1 to each of its numbers.

    Therefore to determine whether a set k consisting of natural numbers is the set of all natural numbers, we have to verify the following two conditions on K:

  1. Does 1 ∈ K?
  2. For each natural number KK; is it true that KK?

    When answer to both the questions is “yes” then K is N. It gives several important principles for establishing the truth of certain classes ...

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