Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By red_dog
  • 1 Post By chiro

Math Help - A weird limit involving e and 1/n

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    A weird limit involving e and 1/n

    Hi, I'm working on a problem but stuck at a weird looking limit:

     \lim _{n \rightarrow \infty } [1- e^{-a-log(n)}]^2

    It is suppose to converge to e^{-e^{-a}} but:

    I wrote the limit as  \lim _{n \rightarrow \infty } [1- \frac {1}{n}- \frac {1}{e^a}]^n

    and as =\lim _{n \rightarrow \infty } [1 + \frac {-1-ne^{-a}}{n}]^n

    But neither are useful as I know the rule is  \lim _{n \rightarrow \infty } (1+ \frac {a}{n} )^n = e^a and I can't seem to get them down to something like that.

    Any hints? Thank you!
    Last edited by tttcomrader; September 20th 2013 at 10:35 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5

    Re: A weird limit involving e and 1/n

    e^{-a-\ln n}=e^{-a}\cdot e^{-\ln n}=\displaystyle \frac{1}{e^a}\cdot\frac{1}{n}=\frac{1}{ne^a}
    Thanks from tttcomrader
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,649
    Thanks
    601

    Re: A weird limit involving e and 1/n

    Hey tttcomrader.

    Hint: e^(-a-log(n)) = e^(-a)/n. Check the limit of lim n-> infinity [1 + b/n]^n (should be e^b if memory serves me correctly).
    Thanks from tttcomrader
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: April 16th 2013, 12:36 AM
  2. Replies: 9
    Last Post: September 8th 2010, 10:15 PM
  3. Really weird limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 16th 2008, 09:32 PM
  4. Weird calculus problem involving
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 11th 2008, 10:06 AM
  5. [SOLVED] A weird limit proof
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 24th 2008, 12:41 PM

Search Tags


/mathhelpforum @mathhelpforum