Find the sum of first n natural numbers.

Find the sum of first n natural numbers.

Sum of n numbers of an AP with first term a and common difference d is =n/2 [2a + (n - 1) d]

The first n natural numbers are =1, 2, 3,.....

First term (a) = 1

Common difference (d) = 3 – 2 = 2 – 1 = 1

The sum of first n natural number is,

S_n = n/2 [2 × 1 + (n - 1) × 1] = n/2 × [2 + n – 1] = n/2 × (n + 1) = (n (n + 1))/2

Hence the sum of first n natural numbers is = (n (n + 1))/2