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

Now that we know the statement is true for n=1, we can use that information (and that information alone) to prove it is true for n=2,3,4,5,...

Now, assume the statement is true for an arbitrary n. We want to use this assumption to show that the statement is true for n+1

While we know the statement is true for n=1, we shouldn't make any assumptions about what other numbers it could be true for