## 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.

*N*contains the natural number 1.*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:*

- Does 1 ∈
*K*? - 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 ...

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