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Thread: Inequalities with Factorials

  1. #1
    Aug 2011

    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.
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  2. #2
    MHF Contributor

    Apr 2005

    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.
    Thanks from topsquark and infraRed
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