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Ratio test.

  1. Oct 26, 2007 #1
    Suppose that [tex]a_n\geq 0[/tex] and there is

    [tex]\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}=c[/tex]
    If c>1,series diverges.
    if c<1 series converges.

    For [tex]a_n=\frac{n!}{n^n}[/tex]

    [tex]\lim_{n\rightarrow\infty}\frac{(n+1)!/(n+1)^{n+1}}{n!/n^n}[/tex]

    [tex]\lim_{n\rightarrow\infty}\frac{n^n}{(n+1)^n}[/tex]

    Then I used I'Hopital Rule and got answer 1.
     
    Last edited: Oct 26, 2007
  2. jcsd
  3. Oct 26, 2007 #2

    Dick

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    I think you'd better check your l'Hopital. Your final limit is closely related to the limit of (1+1/n)^n, which is a famous limit and is not one.
     
    Last edited: Oct 26, 2007
  4. Oct 26, 2007 #3
    A,yes I get it.


    [tex]\lim_{n\rightarrow\infty}\frac{1}{(1+\frac{1}{n})^n}=\frac{1}{e}[/tex]
     
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