In some cases 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 and so on, are all the set of natural numbers.

And the number which is obtained in nature should be a Whole Number and non negative numbers are known as natural number.

‘N’ denotes set of natural numbers.

For example: The set of natural number is n = 4, 5, 6, 7, 8, 9 then calculate the sum of natural numbers.

Solution: Given, the set of natural number:

N = 4, 5, 6, 7, 8, 9;

Then the sum of natural number is:

4;

4 + 5 = 9;

4 + 5 + 6 = 15;

4 + 5 + 6 + 7 = 22;

4 + 5 + 6 + 7 + 8 = 30;

4 + 5 + 6 + 7 + 8 + 9 = 39;

And the formula for finding the sum of ‘n’ natural numbers:

S

_{n}=

__n (n + 1),__

2

Where, ‘n’ is the total given number.

In the above example the value of n = 6.

So put the value of n in the given formula we get:

S

_{n}=

__n (n + 1),__

2

S

_{n}=

__6(6 + 1),__

2

Now we add the value which is present in the bracket.

S

_{n}=

__6(7),__

2

S

_{n}=

__42,__

2

S

_{n}= 21.

The sum of ‘n’ natural numbers is 21.