Business Mathematics

25

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 K ∈ K; is it true that K ∈ K?

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