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

Look at the base case n=1. The sum of the first 1 odd natural numbers (which is just 1) is 1, and 1²=1. So the base case has been verified, and we can move on to the induction step

Look at the base case n=2. The sum of the first 2 odd natural numbers (1 and 3) is 4, and 2²=4. So the base case has been verified, and we can move on to the induction step

Look at the base case n=3. The sum of the first 3 odd natural numbers (1,3,5) is 9, and 3²=9. So the base case has been verified, and we can move on to the induction step