Depending on the properties and how the numbers are represented in the number line, they are classified into different types. They are natural numbers, whole numbers, integers, real numbers, rational numbers, irrational numbers, complex numbers, imaginary numbers and so on. Each division of numbers has a different set of properties and usages.

Natural numbers signify a part of the number system which covers all the positive integers from 1 to infinity and are also applied for counting purposes. Natural numbers do not include zero (0). The series 1,2,3,4,5,6,7,8,9…., is also termed as counting numbers. Natural numbers are also a section of real numbers, that involve only the positive integers i.e. 1, 2, 3, 4,5,6, ………. excluding zero, fractions, decimals and negative numbers.

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What is Sum of Natural Numbers?

Sum of natural numbers or the sum of n numbers is obtained by practicing the arithmetic progression formula wherein the common difference between the preceding and succeeding numbers is equal to one. Let us read about the sum of n natural numbers formulas with derivation and a few solved examples.

Sum of n natural numbers formula is applied to determine the summation of 1 + 2 + 3 + 4 +….. up to n terms. These numbers are arranged in an arithmetic sequence. Therefore we use the formula of the sum of n terms in the arithmetic progression for determining the formula for the sum of natural numbers.

The sum of the first n natural number is given by the formula:

where n is the natural number.

The sum of first n natural numbers as read above can be defined with the help of arithmetic progression. Where the sum of n terms is organized in a sequence with the first phase being with 1 and n being the number of terms along with the nth term.

Natural numbers include whole numbers in them except the number 0.

Derivation of Sum of Natural Numbers Formula

So far we have read about the definition and formula. Now let us derive the sum of natural numbers applying the sum of n terms in an AP. In arithmetic progression AP, ‘a’ signifies the first term, ‘d’ denotes a common difference, ‘l’ is the last term.

Examples on Sum of n Natural Numbers

With the knowledge of definition and formula for sum of natural numbers let us practice some examples for more understanding:

Examples 1: Find the sum of the first 100 natural numbers?

Solution: We can practice the arithmetic progression formula to obtain the sum of the first 100 natural numbers. Where a = 1, n = 100, and d = 1.

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