How to Evaluate 4!!!!Date: 10/16/2003 at 17:38:14 From: liz Subject: 4!!!! Is there a resource in any books that could give me the exact value for 4!!!!? Our Calculus 2 teacher has challenged us to find the answer, but the number is too large to reasonably calculate by hand: 4! = 24 24! = I really appreciate any help that you could provide! Date: 10/16/2003 at 19:07:43 From: Doctor Shawn Subject: Re: 4!!!! Liz, 4!!!! is too big to even reasonably calculate with good computer software. You might want to check out this archived answer: Googol! http://mathforum.org/library/drmath/view/57903.html The thing is, your number is going to be much larger even than any of the numbers under discussion. 24! is about 6.20448402 x 10^23; taking the factorial of that explicitly is more or less beyond any feasible computer or calculator; and taking the factorial of THAT explicitly would require more time than can exist. I think the purpose of this assignment is to show you how fast the factorial function explodes. You can use the techniques on that page to attempt an approximation, but it won't be very accurate. Does that help? - Doctor Shawn, The Math Forum http://mathforum.org/dr.math/ Date: 10/17/2003 at 12:41:49 From: Doctor Douglas Subject: Re: 4!!!! Hi Liz, Thanks for writing to the Math Forum. I'd like to supplement Dr. Shawn's answer. There are different ways to interpret multiple factorial signs. One way, of course, is 3!!! = ((3!)!)! = ((6)!)! = 720! Another way is to do the following: n! = n(n-1)(n-2)... the usual factorial n!! = n(n-2)(n-4)... e.g. 5!! = 5*3*1 = 15 "double factorial" n!!! = n(n-3)(n-6)... n!!!! = n(n-4)(n-8)... etc., where the products run only over positive integers. This is called "multifactorial" notation. You can read more about it here: Eric Weisstein's World of Mathematics -- Multifactorial http://mathworld.wolfram.com/Multifactorial.html - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ Date: 10/20/2003 at 03:54:48 From: liz Subject: Thank you (4!!!!) Thanks for the info! |
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