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Solve the inequality problem

  1. Jul 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve the inequality,

    [tex]\frac{1.8^n}{n!}<0.201[/tex]


    2. Relevant equations



    3. The attempt at a solution

    some hints?
     
  2. jcsd
  3. Jul 14, 2010 #2

    lanedance

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    Re: inequality

    have you considered Stirlings approximation for the factorial?
     
  4. Jul 14, 2010 #3

    lanedance

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    Re: inequality

    for n>>1
    [tex] n! \approx \sqrt{2 \pi n} \left( \frac{n}{e} \right)^n [/tex]
     
    Last edited: Jul 14, 2010
  5. Jul 14, 2010 #4

    lanedance

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    Re: inequality

    though you'll have to check that n is pretty big... clearly n>8 here but how big...?
     
  6. Jul 14, 2010 #5
    Re: inequality

    n=6, is 6 considered large?
     
  7. Jul 14, 2010 #6

    lanedance

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    Re: inequality

    no sorry, i though it was 8^n...

    can you just use brute force then & test n values?
     
  8. Jul 14, 2010 #7
    Re: inequality

    yeah, that's how i got n=6 but i just wonder is there a tidier and definite way of solving that.
    Thanks for helping me thus far.
     
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