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Limit of factorial

  1. Apr 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine the divergence or the convergence of the sequence. If it converges find its limit.

    a[tex]_{n}[/tex] = ([tex]\frac{(n)!}{2n!+1}[/tex])


    3. The attempt at a solution

    All I know about factorials is for example 4! = 1*2*3*4. So as far as limits go I'm clueless. please help!
     
  2. jcsd
  3. Apr 7, 2009 #2
    I like to think of limits this way. First intuatively say why it should converge or diverge, then apply the intuation in a rigorous way. In this case both top and bottom are about the same thing so you would expect it to converge. How to say this in a formal manner? Use an inequality that will enable you to cancel the factorials and use the theorem that says if [itex]0 \leq a_n \leq b_n[/itex] for each n, then if b_n converges, so does a_n.
     
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