Number System

Natural Numbers – Numbers used in counting are known as natural numbers.

Whole Numbers – Natural Numbers with zero are known as whole numbers.

Prime Numbers – Numbers that are not divisible by other numbers except the number itself and 1 are known as prime numbers.

Composite numbers – Numbers other than the one which are not prime are known as composite numbers.

Even Numbers – Numbers that are divisible by 2 are known as Even numbers.

Odd Numbers – Numbers that are not divisible by 2 are known as odd numbers.

Consecutive numbers – Numbers increasing by one are known as consecutive numbers.

Integers – Negative numbers and whole numbers together are known as integers.

Rational Numbers – Numbers in the form P/Q are known as rational numbers. Here, P and Q are integers and Q is not zero.

Irrational Numbers – Numbers that cannot be represented in the form P/Q are known as irrational numbers.

Real Numbers – Real numbers consists of both rational as well as irrational numbers.

Formulae:

Sum of first n natural numbers = $\frac{n(n+1)}{2}$

Sum of first n odd numbers = $n \times n = n^2$

Sum of first n even numbers = $n(n+1)$

Sum of squares of first n natural numbers = $\frac{n(n+1)(2n+1)}{6}$

Sum of cubes of first n natural numbers = $[\frac{n(n+1)}{2}]^2$