NUMBERS

Chapter-1

NUMBERS

• Natual numbers are the numbers used for counting N=❴1,2,3,4,........❵
• Whole number consist of nutural number and zero W=❴0,1,2,3,4,.. ..❵
• Integers are the best off all counting numbers,their negatives and zero.I=❴...-3,-2,-1,0,1,2,3,4,...❵  
• Rational numbers the numbers which can be   written in the form p/q where p ,q are integers and    q≠0 [e.g 1/2 ,8/9 ]
• Irrational numbers cannot be expressed in the form p/q  e.g   (√2=1.414....,  √3=1.732......
• Prime number is a number which has no factors other than 1 and itself (e.g 2,3,13) ,2 is the  smallest prime number as well as the only ever prime number.

Important formulas
1:Sum of first "n" Natural numbers =n❲ n+1 ∕ 2 ❳

2:Sum of first "n" Odd numbers =n²

3:Sum of first "n" even numbers =n(n+1)

4: 1²+2²+3²+........n(n+1)(2n+1)/6

5: 1³+2³+3³+........[n(n+1)/2]

6:Product of two numbers=Product of their HCF and LCM