Math geeks only

[Ghoulish Delight]

- OR -

Yes, I am geeky enough to be kept awake at night by number theory


I need some formal proof help. Never my strong suit. I grasp the general concept, but when it comes to being properly formal and pedantic, I get a bit fuzzy.

What I'm struggling with now is whether a certain kind of deductive conclusion is permissable, or if I need more rigor.

What I'm trying to prove is that for any integer value of n > 2, n*7 < 10^(n-1).

It's certainly a true statement, but I'm trying to formalize it. The best I've come up with is to know that for the value n=3 it is true and that the expression on the left grows linearly while the expression on the right grown exponentially.

Is that sufficient proof? That given any 2 functions f and f` such that f(n) < f`(n) AND f grows linearly while f` grows exponentially, f(x) < f`(x) for all values > n?