The sum of first n odd natural numbers is

The sum of the first n odd numbers forms an arithmetic progression with first term equal to 1 and the last term equal to 2(n−1) + 1

The formula for an arithmetic progression of n terms with first term a1 and last term a_n is

(a₁ + a_n)

Substituting these values, a₁=1, a_n= 2(n−1) + 1

⇒ n (1 + 2n−2 + 1)2 = n (2n) 2= n²