Results 1 to 2 of 2

Math Help - Converging Sequence!! AKA Infinite Series!!

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    4

    Exclamation Converging Sequence!! AKA Infinite Series!!

    Question:

    Show that the sequence is convergent by computing its limit when n -> ∞

    a(n) = (e^-n)/[1-n^(1/n)]



    Related Equations:

    lim [n -> ∞] a(n) = L


    My Attempt:

    I tried using l'hopitals rule however it does not work.
    Any suggestions???
    Last edited by olyviab1; March 25th 2010 at 09:25 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by olyviab1 View Post
    Question:

    Show that the sequence is convergent by computing its limit when n -> ∞

    a(n) = (e^-n)/[1-n^(1/n)]


    Related Equations:

    lim [n -> ∞] a(n) = L


    My Attempt:

    I tried using l'hopitals rule however it does not work.
    Any suggestions???


    Hint: since clearly n>\left(1+\frac{1}{n}\right)^n\,\,\,\forall\,3<n\i  n\mathbb{N} ,we get \sqrt[n]{n}>1+\frac{1}{ n} , and thus:


    0\leq \frac{e^{-n}}{n^{1\slash n}-1}\leq \frac{e^{-n}}{1\slash n} =\frac{n}{e^n} , and this last limit is zero by L'H. rule ... and yes, I know the denominator is twisted, but it never minds.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: July 18th 2010, 06:59 PM
  2. Sequence converging to Zero.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 28th 2009, 09:41 AM
  3. Replies: 7
    Last Post: October 12th 2009, 10:10 AM
  4. Converging and Diverging Infinite Series help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 15th 2009, 05:06 AM
  5. converging sequence?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 29th 2009, 02:46 PM

Search Tags


/mathhelpforum @mathhelpforum