Want to show: the sum of the first n natural numbers equals n(n+1)/2

Check the base case of n=1. Since the sum of the first 1 natural numbers (which is just 1) equals 1 and 1(1+1)/2=1, we verify the base case and can now move on to the induction step

Check the base case of n=2. Since the sum of the first 2 natural numbers (1 and 2) equals 3 and 2(2+1)/2=3, we verify the base case and can now move on to the induction step

Check the base case of n=5. Since the sum of the first 5 natural numbers (1,2,3,4,5) equals 15 and 5(5+1)/2=15, we verify the base case and can now move on to the induction step