1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit of series

  1. Aug 20, 2008 #1
    1. The problem statement, all variables and given/known data
    what is the limit of this expression?

    [tex]lim_{n\rightarrow\infty}\frac{n^n}{n!}[/tex]

    2. Relevant equations



    3. The attempt at a solution
    I tried to make it look like [tex]\frac{x^n}{n!}[/tex] and also tried to apply the sandwich theorem, but got nothing logical.
    Probably the limit is [tex]\infty[/tex], still I want to prove it mathematically.
     
  2. jcsd
  3. Aug 20, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You could take the log and use Stirling's approximation on the factorial.
     
  4. Aug 20, 2008 #3
    Could you show it explicitly?
     
  5. Aug 20, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you mean show the details, Isn't that your job? Did you look up Stirling's approximation? Or do you mean do it without Stirling's formula?
     
  6. Aug 20, 2008 #5
    if you take the stirling's approximation there is no need to take log of the term on numerator.
    that why i asked that.
     
  7. Aug 20, 2008 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Right, if you use the form n!~(n/e)^n. I was thinking of ln(n!)~n*ln(n)-n
     
  8. Aug 20, 2008 #7
    thanks for the post
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Limit of series
  1. Limit of a series (Replies: 3)

  2. Series Limit (Replies: 1)

  3. Limit of a series (Replies: 5)

  4. The limit of a series (Replies: 5)

Loading...