Almost. We assume that there exists some number K such that holds. (We could also use "strong induction" and assume that there is a number K such that for all , but we don't need anything like that here.)

Now we need to show that

Look at the LHS:

By hypothesis , so we know that

So

Now, how does compare to ? It is greater, of course. So we have, finally:

or

Since the theorem is true for K = 2, it is true for K = 3, 4, ...

-Dan