Alright problem is pretty simple, I have two functions(adsbygoogle = window.adsbygoogle || []).push({});

f(x) = n!

g(x) = 2^n

Question is to show that g(x) = Of(x) through mathematical expression

that is show the growth rate of g(x) <= that of f(x)

The fact that this is true is fairly obvious, it's bigger for n>3.

Anyway my problem is I only know how to define n! as a recursive definition, so I'm not really sure how to demonstrate this truth in any kind of mathematical way. If you put both as a reiman product or whatever it's called (ie n-i for i=0 to n and 2 for i=0 to n) you have a function compared to a number.

like

2*2*2*2*....*2 (n terms)

1*2*...*(n-1)*(n) (n terms)

I don't really wanna use induction since I dont think it's necessary or expected, and I don't really know how to do the inductive step since one of the functions has no variables.

Anyway any ideas? Or anyone know a non recursive definition for factorial so I can compare it to 2^n? heh

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# Homework Help: Function Growth Rates

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