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Math Help - factorials

  1. #1
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    factorials

    Solve for N:

    7!8!9!/7!+8!+9!=8!N!/9
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  2. #2
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    Re: factorials

    Quote Originally Posted by rubytuesday View Post
    Solve for N:

    7!8!9!/7!+8!+9!=8!N!/9
    noting the lack of parentheses in your equation, do you really mean this ...

    \frac{7! \cdot 8! \cdot 9!}{7! + 8! + 9!} = \frac{8! \cdot n!}{9}

    ???
    Last edited by skeeter; November 15th 2011 at 07:02 PM.
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  3. #3
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    Re: factorials

    Hello, rubytuesday!

    \text{Solve for }N:\;\;\frac{7!\,8!\,9!}{7!+8!+9!} \:=\:\frac{8!\,N!}{9}

    We have: . \frac{8!\cdot N!}{9} \;=\;\frac{7!\cdot8!\cdot9!}{7!+8!+9!}

    . . Note that: . 7! + 8! + 9! \;=\;7!(1 + 8 + 8\!\cdot\!9) \;=\;7!(81)

    So we have: . \frac{8!\cdot N!}{9} \;=\;\frac{\rlap{//}7!\cdot 8!\cdot 9!}{\rlap{//}7!\cdot 9^2} \;=\;\frac{8!\cdot9!}{9\cdot 9} \;=\; \frac{8!\cdot(8!\cdot\rlap{/}9)}{9\cdot \rlap{/}9}

    . . . . . . . . . . \frac{8!\cdot N!}{9} \;=\;\frac{8!\cdot 8!}{9}

    Multiply by \frac{9}{8!}\!:\;\;N! \;=\;8! \quad\Rightarrow\quad \boxed{N \:=\:8}

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  4. #4
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    Re: factorials

    Thank You!
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