Want to show: Prove that the sum of the first n odd natural numbers equals n²

Now assume the statement is true for arbitrary n (i.e, the sum of the first n odd natural numbers is n²). Since n is arbitrary, we should consider separate cases of if n is prime or not.

Now assume the statement is true for arbitrary n (i.e, the sum of the first n odd natural numbers is n²). Add n+1 to get a new formula for the sum of the first n+1 odd natural numbers

Now assume the statement is true for arbitrary n (i.e, the sum of the first n odd natural numbers is n²). Add 2n+1 to get a new formula for the sum of the first n+1 odd natural numbers