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Find the limit

  1. Dec 29, 2004 #1
    Hi ,

    Evaluate the following limit :

    [tex]\lim_{n\rightarrow\infty}\frac{n}{(n!)^{\frac1n}}=\lim_{n\rightarrow\infty}\frac{n}{\sqrt[n]{n!}}[/tex]
     
    Last edited: Dec 29, 2004
  2. jcsd
  3. Dec 29, 2004 #2

    NateTG

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  4. Dec 30, 2004 #3
    I know about that .. the solution will be obtained easily by that method ..



    but.. could you solve the question without stirling's approximation ?
     
    Last edited: Dec 30, 2004
  5. Dec 30, 2004 #4

    dextercioby

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    I'm afraid Stirling's approximation provides the simplest approach.Keep in mind that u've to compute the limit of a sequence and u cannot make the transition to a function,due to a factorial in the denominator.Of course,that factorial can be put under the form
    [tex] n!=\Gamma(n+1) [/tex]
    ,but that won't do you any good,since it still involves discrete values for "n".

    Daniel.
     
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