EVEN & ODD NUMBERS

INTRODUCTION:

  

According to divisibility by 2 the Natural numbers are classified into two types 

                                          1. Even natural numbers

                                          2. Odd natural numbers

EVEN NUMBERS:

  

      The numbers which are divisible by 2 are called even numbers.

                                            or

       The numbers with 0,2,4,6,8 at the ones place are called even numbers.

    👉 The set of even numbers is denoted by  E

    👉 i.e.,  E= {2, 4, 6, 8, 10, 12, 14,...}

Example: 2024, 5689720, 698456324, etc

  

NOTE 👍

 The general form of even numbers =2n ( where n is any natural number)

NOTE 👍

 The sum of first n even natural numbers = n(n+1)

Example: Find the sum of first 20 even numbers?

Here n=20 

Sum of first 20 even numbers = 20 (20 +1)

                                                    = 20 X 21

                                                    =420

ODD NUMBERS:

  

      The numbers which are not divisible by 2 are called odd numbers.

                                            or

       The numbers with 1,3,5,7,9 at the ones place are called odd numbers.

    👉 The set of odd numbers is denoted by  O.

    👉 i.e.,  O= {1, 3, 5, 7, 9, 11, 13,...}

Example: 2023, 5689721, 698456325, etc

  

NOTE 👍

 The general form of odd numbers =2n-1 ( where n is any natural number)

NOTE 👍

 The sum of first n odd natural numbers = n²

Example: Find the sum of first 20 odd numbers?

Here n=20 

Sum of first 20 odd numbers = 20²

                                                  = 400

Properties of even & odd numbers:

 

EVEN + EVEN = EVEN	EVEN – EVEN = EVEN	EVEN x EVEN = EVEN
ODD  + ODD = EVEN	ODD – ODD = EVEN	ODD x ODD = ODD
EVEN + ODD = ODD	EVEN – ODD = ODD	EVEN x ODD = EVEN

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