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- Number Series - NS
- Note
- Logical Reasoning
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Natural Numbers : Numbers which are used for counting the objects are called natural numbers. They are denoted by N. N = { 1, 2, 3………………..} All positive integers are natural numbers. Whole numbers :- When ‘zero’ is included in the natural numbers, they are known as whole numbers. They are denoted by W. W= { 0, 1, 2, 3……………….} Integers : All natural numbers, zero and negatives of natural numbers are called as integers. They are denoted by I. I = { ………………..,-3, -2, -1, 0, 1 , 2, 3………………} Rational numbers : The numbers which can be expressed in the form of are integers and are called rational numbers where P and Q They are called by Q. Irrational numbers : The numbers which cannot be written in the form of Q are integers and are called irrational numbers. where P and When these numbers are expressed in decimal form, they are neither terminating nor repeating. Number System Page 1

Real numbers : Real numbers include both rational as well as irrational numbers. Positive or negative, large or small, whole numbers or decimal numbers are all real numbers. e.g.= 1, 13.79, -0.01, etc. Imaginary numbers : An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit ‘i’ which is defined by its properly Note : Zero (0) is considered to be both real and imaginary number. Prime number : A prime number is a natural number greater than 1 and is divisible only by 1 and itself. e.g.2, 3, 5, 7, 11, 13, 17 ,19 ………….etc. Note :- 2 is the only even prime number. Composite Numbers : A number, other than 1, which is not a prime number is called a composite number . E.g. 4, 6, 8, 9, 10, 12, 14, 15 ……….etc. Note :1 1 is neither a prime number nor a composite number. 2 there are 25 prime numbers between 1 and 100. To find whether a number is prime or notTo check whether the number is prime or not, 1 We take an integer larger than the square root of the number. Let the number be ‘k’. 2 Test the divisibility of the given number by every prime number less than ‘k’. 3 If it is not divisible by any of them, then the given number is prime otherwise it is a composite number. E.g.= Is 881 a prime number ? Sol- The appropriate square root of 881 is 30. Number System Page 2

Prime number less than 30 are 2, 3, 5, 7, 11, 13, 17,19, 23,29. 881 is not divisible by any of the above numbers, so it is a prime minister. Co-prime numbers : Two numbers are co-prime of their HCF is 1. E.g. (2,3), (3,4) , (5,7), (3,13) etc. Even numbers : The number which is divisible by 2 is called even number. E.g. – 2, 4, 6, 8……………. Odd numbers – The number which is not divisible by 2 is called odd number. e.g.= 3, 5, 7, 9………….. Consecutive numbers : A series of numbers in which the succeeding number is greater then the preceding number by 1 is called a series of consecutive numbers. i.e., Difference between two consecutive numbers is 1. Some Rules on Counting Numbers 1. Sum of all the first n natural numbers Q. Find the sum of first 20 natural numbers. Ans- Sum of 1 to 20 Q. Find the sum of numbers from 11 to 20. Number System Page 3

2. Sum of first n old numbers = Q. What is the sum of first 10 odd numbers ? Ans- Sum of first 10 odd numbers = Q. Find the sum of 9+11+13+………+29 Ans – 1+3+5+…………+29= (as there are 15 odd numbers from 1 to 29) 1+3+5+7= 9+11+13+29=225-16=209 3. Sum of first n even numbers Q. What is the sum of even numbers between 1 and 50 ? Q. Find the value of 12+14+……….+30. Ans- (2+4+6+…….+30) has 15 even numbers Number System Page 4

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