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Homework Help: Limit using theorems

  1. Sep 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Prove using limit theorems that

    [tex] lim \frac{10^n}{n!} = 0 [/tex]

    2. Relevant equations
    We get to use limit theorems. These include
    1 lim(a+b) = lim a + lim b,
    2 lim(ab) = lim(a)lim(b),
    3 lim(s_n) = [tex] \infty [/tex] iff lim(1/s_n)= 0,
    4 lim(ks_n) = k*lim(s_n)
    5 if lim(s_n) = [tex] \infty [/tex] and lim(t_n) equals some real number, then lim(s_n*t_n) = [tex] \infty [/tex]

    3. The attempt at a solution
    I am having difficulty figuring out how to manipulate the factorial to match a theorem. Any advice/hints would be appreciated. Thanks.
    Last edited: Sep 30, 2007
  2. jcsd
  3. Sep 30, 2007 #2


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    Homework Helper

    What does the limit approach? (n---> ?) well expand out n! as n(n-1)(n-2)*...*3*2*1 and see if that helps
  4. Sep 30, 2007 #3
    n approached infinity. But what you said did it. Thanks.
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