Results 1 to 2 of 2

Math Help - Series Convergence

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Series Convergence

    Find all x for which

    \displaystyle\sum\limits_{n=1}^\infty n^nx^n

    Attempt: Ratio Test

    \lim_{x \to +\infty} |\frac {(n+1)^{n+1}x^{n+1}}{n^nx^n}|

    =(\frac{n+1}{n})^n(n+1)|x|

    =(1+\frac{1}{n})^n(n+1)|x|

    =e(n+1)|x|

    Where do I go from here?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    For x\neq 0 we have

    \displaystyle\lim_{n\to +\infty}\left(1+\dfrac{1}{n}\right)^n(n+1)|x|=+\in  fty

    So, the series is convergent iff x=0 .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 3rd 2011, 02:12 AM
  2. Replies: 2
    Last Post: May 1st 2010, 10:22 PM
  3. Replies: 4
    Last Post: December 1st 2009, 04:23 PM
  4. Replies: 3
    Last Post: December 1st 2009, 04:06 PM
  5. series convergence and radius of convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2008, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum