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Mathematics 22 Online
OpenStudy (varaug):

what is !100?

OpenStudy (smartperson):

i don't understand your question

OpenStudy (varaug):

!100 is 100 *99*98*97 etc

OpenStudy (solomonzelman):

\(\color{blue}{n!=1\times 2\times 3\times 4\times }\) \(\color{blue}{...}\) \(\color{blue}{(n-2)\times (n-1)\times n }\) For example, \(\color{blue}{5!=1\times 2\times 3\times 4\times 5= 120}\)

OpenStudy (varaug):

don't know why my college would make me solve such an ungodly question but hey,

OpenStudy (solomonzelman):

So, essentially, a factorial of \(n\) (where n is a positive integer), is equal to the product of all positive integers from 1 to n.

OpenStudy (solomonzelman):

So, a \(\color{blue}{100!}\) is a product of all natural numbers up to 100.

OpenStudy (varaug):

yes, i know this, i just want some help solving it since i know the answer is huge.

OpenStudy (solomonzelman):

Yes, the answer is huge, and there isn't a way to simplify it. (Unless \(\color{blue}{100!}\) is not your entire question)

OpenStudy (varaug):

just too big huh?

OpenStudy (solomonzelman):

So, if you had \(\color{blue}{\displaystyle \frac{100!}{98!}}\), then THAT would have a relevantly small answer.

OpenStudy (solomonzelman):

But, just \(100!\) (alone - if there isn't more to this question, then it) is that huge answer.

OpenStudy (varaug):

hmm thanks. i swear, on my free time, I'm going to make a goal to solve 100! if its the last thing i do! XD

OpenStudy (solomonzelman):

\(\color{blue}{\displaystyle \Gamma(101)=100!={\rm that~huge~number}}\)

OpenStudy (solomonzelman):

well, gamma for natural integers is same.

OpenStudy (varaug):

kool. (so i spelled it wrong, grammar police come get me i dare ya)

OpenStudy (solomonzelman):

I'd give you a virtual slap if I was your English T-shirt. (Did I say it correctly?:))

OpenStudy (varaug):

*sticks nose up defiantly* nu!

OpenStudy (solomonzelman):

:))

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