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Math Help - Simplify the factorial expression

  1. #1
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    Simplify the factorial expression

    Simplify the factorial expression

    (3n + 1)! / (3n)! and (n+2)! / n!




    ok i know how to simplify 4!/6! which is 1/30 but when they have the letter n in the problem i dont know where to start. man im getting tire been at this since 4 pm lol
    Last edited by flexus; September 26th 2009 at 10:08 PM. Reason: none
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by flexus View Post
    Simplify the factorial expression

    (3n + 1)! / (3n)! and (n+2)! / n!




    ok i know how to simplify 4!/6! which is 1/30 but when they have the letter n in the problem i dont know where to start. man im getting tire been at this since 4 pm lol
    \frac{(3n+1)!}{(3n)!}=\frac{(3n+1){\color{red}(3n)  (3n-1)\cdots(2)(1)}}{(3n)!}=\frac{(3n+1)\cdot(3n)!}{(3  n)!}=3n+1.

    Does this make sense?

    Try to do something similar for the second one.
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    \frac{(3n+1)!}{(3n)!}=\frac{(3n+1){\color{red}(3n)  (3n-1)\cdots(2)(1)}}{(3n)!}=\frac{(3n+1)\cdot(3n)!}{(3  n)!}=3n+1.

    Does this make sense?

    Try to do something similar for the second one.
    ok i see that the (3n)! canceled out but how did you get (3n)(3n-1)...(2)(1) and then where did it go??
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by flexus View Post
    ok i see that the (3n)! canceled out but how did you get (3n)(3n-1)...(2)(1) and then where did it go??
    I got that because that is how factorial is defined!

    (3n+1)!=(3n+1)(3n)(3n-1)(3n-2)\cdots(3)(2)(1)

    But that's the same as saying (3n+1)!=(3n+1)\cdot(3n)! - Hence why we got cancellation towards the end of the problem.
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  5. #5
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    Quote Originally Posted by Chris L T521 View Post
    I got that because that is how factorial is defined!

    (3n+1)!=(3n+1)(3n)(3n-1)(3n-2)\cdots(3)(2)(1)

    But that's the same as saying (3n+1)!=(3n+1)\cdot(3n)! - Hence why we got cancellation towards the end of the problem.
    your probably gonna get angry if i told you i didnt understand that so im gonna go youtube factorials and ill get back to this problem. thank you for trying to explain. your help was greatly appreciated.
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  6. #6
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    Quote Originally Posted by Chris L T521 View Post
    I got that because that is how factorial is defined!

    [snip]
    And defined! = (defined)(efined)(fined)(ined)(ned)(ed)(d)
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