What is the sum of n natural numbers 1 2 n

Sum of the First n Natural Numbers

We prove the formula 1+ 2+ … + n = n(n+1) / 2, for n a natural number. There is a simple applet showing the essence of the inductive proof of this result.

Definition of Sum of n Natural Numbers

The sum of n natural numbers is represented as [n(n+1)]/2. Natural numbers are the numbers that start from 1 and end at infinity. Natural numbers include whole numbers in them except the number 0.

The formula n(n−1)/2 for the number of pairs you can form from an n element set has many derivations, even many on this site. One is to imagine a room with n people, each of whom shakes hands with everyone else. If you focus on just one person you see that she participates in n−1 handshakes.

Also, the sum of first ‘n’ positive integers can be calculated as, Sum of first n positive integers = n(n + 1)/2, where n is the total number of integers. Let us see the applications of the sum of integers formula along with a few solved examples.

The formula of the sum of first n natural numbers is S=n(n+1)2 .

Following is the representation to find the sum of n natural numbers using the mathematical formula: Sum of n natural number = n * (n + 1) / 2.

Sum of Squares of n Natural Numbers Formula

Natural numbers include whole numbers in them except the number 0. If we need to calculate the sum of squares of n consecutive natural numbers, the formula is Σn² = n×(n+1)×(2n+1)6 n × ( n + 1 ) × ( 2 n + 1 ) 6 .