Results 1 to 3 of 3

Math Help - Show a function series converges

  1. #1
    Senior Member Twig's Avatar
    Joined
    Mar 2008
    From
    Gothenburg
    Posts
    396

    Show a function series converges

    Hi!

    Problem: Show that \sum_{n=1}^{\infty}xe^{-nx} is convergent for x\geq 0 .Also show that the convergence is uniform on every interval  \left(a,\infty\right) , where a>0 .

    Is the convergence uniform on  \left(0,\infty\right) ?

    I would appreciate a fairly detalied solution, explaining most of the steps.

    Thx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Aug 2009
    Posts
    143
    Quote Originally Posted by Twig View Post
    Hi!

    Problem: Show that \sum_{n=1}^{\infty}xe^{-nx} is convergent for x\geq 0 .Also show that the convergence is uniform on every interval  \left(a,\infty\right) , where a>0 .

    Is the convergence uniform on  \left(0,\infty\right) ?

    I would appreciate a fairly detalied solution, explaining most of the steps.

    Thx
    The series is essentially a geometric series.
    Last edited by mr fantastic; September 19th 2009 at 01:22 AM. Reason: Restored original reply
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Twig's Avatar
    Joined
    Mar 2008
    From
    Gothenburg
    Posts
    396
    Quote Originally Posted by luobo View Post
    The series is essentially a geometric series.
    With e^{x} .

    So I get x \cdot \sum_{n=1}^{\infty}\frac{1}{\left(e^{x}\right)^{n}  }

    Alright, thx.
    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. How do I show the series of an*bn converges?
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 24th 2011, 05:59 PM
  3. Function series which converges uniformly but not absolutely
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: February 3rd 2010, 01:35 PM
  4. How to show this converges to 0
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 15th 2009, 02:35 PM
  5. Show a series converges for any x
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 25th 2006, 12:29 AM

Search Tags


/mathhelpforum @mathhelpforum