Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rudin's explanation of how rapid the series 1/(n!) converges

  1. May 6, 2013 #1
    In Rudin's Principle's of Mathematical Analysis, Rudin days that we can estimate how fast the series [itex]\sum\frac{1}{n!}[/itex] converges by the following:
    so that
    The part that bothers me is
    Using Maple I was able to see that
    but what if I did not have access to anything like Maple or Mathematica. How would I be able to figure out that the equality holds?
  2. jcsd
  3. May 6, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    That sum is a geometric series - do you know what to do with those?
  4. May 6, 2013 #3
    Oh. HAHAHAHA. Wow. Okay. I see it now. Thanks.
  5. May 6, 2013 #4


    User Avatar
    Science Advisor

    The sum is simply a geometric series with r = 1/(n+1), so the sum = 1/(1-r) = (n+1)/n.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Rudin's explanation rapid
I Proof that p is interior if p is not limit of complement