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Which function grows faster?

  1. Jun 24, 2009 #1
    [tex]n^n[/tex]

    or

    [tex]\prod_{r=0}^{n-1}\left(\begin{array}{c}\sum_{j\leq r}\left(\begin{array}{c}n\\ j\end{array}\right)\\2^r\end{array}\right)[/tex]

    Asymptotically, I mean.
     
    Last edited: Jun 25, 2009
  2. jcsd
  3. Jun 25, 2009 #2

    CRGreathouse

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    Since
    [tex]\prod_{r=0}^{n-1}{{\sum_{j<r}{n\choose j}}\choose{2^r}}={0\choose1}\prod_{r=1}^{n-1}{{\sum_{j<r}{n\choose j}}\choose{2^r}}=0[/tex]
    I'd have to go with [itex]n^n[/itex].
     
  4. Jun 25, 2009 #3
    How about now?
     
  5. Jun 25, 2009 #4

    CRGreathouse

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    It seems that the product grows faster.
     
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