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Solving for N

  1. Jun 10, 2009 #1
    1. The problem statement, all variables and given/known data

    I need to find N:

    {[pi^(N+1)] / (N+1)!} . {1/2^N} <= 10^-5

    2. Relevant equations

    3. The attempt at a solution

    I'm really struggling with this, i think taking logs is involved, but i can't seem to find a value of N.

    Any help?
  2. jcsd
  3. Jun 10, 2009 #2


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    The expression decreases with increasing N. You basically want to evaluate it for various values of N until you figure out where it starts going below 10^(-5). You can only estimate log(n!) and the estimate doesn't lead to anything you can really solve.
  4. Jun 10, 2009 #3


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    Do you need to find any N, or the smallest such N?
  5. Jun 10, 2009 #4
    I need to find what N needs to be bigger or equal to.
  6. Jun 10, 2009 #5


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    Then just try some integer values for N. N doesn't have to be very big.
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