# Math Help - Inequalities with Factorials

1. ## Inequalities with Factorials

Can one solve inequalities with factorials, without simply guessing with a calculator? A common example:

n! > 1000

Obviously, I could simply calculate with values of N until I get one that works. But I'm wondering if there is a more direct way.

2. ## Re: Inequalities with Factorials

I assume you mean "a faster way". Calculating values of n! for values of n seems to me to be the "direct" way! I presume you know that 6!= 6(5)(4)(3)(2)= 120(6)= 720 so 7!= 7(6!)= 7(720).

As for really big numbers (1000 is NOT "really big"!), you can get an approximate solution by using Strirlings formula: n! is approximately equal to $\sqrt{2\pi n}\left(n/e\right)^n$.