Results 1 to 4 of 4

Math Help - Function series pointwise convergence question

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    2

    Function series pointwise convergence question

    does the following converge pointwise? help pls


    x's domain:
    0<=x<infinity
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Abu-Khalil's Avatar
    Joined
    Oct 2008
    From
    Santiago
    Posts
    148
    Let x\in\mathbb{R}\Rightarrow \exists k\in\mathbb{N}:x\leq k. Hence

    \sum_{n=k}^\infty e^{-|x-n|}=\sum_{n=k}^\infty e^{-n+x}=e^x\sum_{n=k}^\infty e^{-n}=e^{x-k}\sum_{n=0}^\infty e^{-n}<\infty.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    2

    a little explanation pls

    why is this pass true? :

    \sum_{n=k}^\infty e^{-|x-n|}=\sum_{n=k}^\infty e^{-n+x}<br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Abu-Khalil's Avatar
    Joined
    Oct 2008
    From
    Santiago
    Posts
    148
    Quote Originally Posted by tomersbar View Post
    why is this pass true? :

    \sum_{n=k}^\infty e^{-|x-n|}=\sum_{n=k}^\infty e^{-n+x}<br />
    If n\geq k\Rightarrow n-x\geq k-x\geq 0\Rightarrow |x-n|=n-x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Uniform convergence vs pointwise convergence
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 16th 2012, 12:03 AM
  2. Fourier series (pointwise convergence)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 5th 2010, 09:03 AM
  3. proving pointwise convergence for piecewise function
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 9th 2010, 07:36 PM
  4. Pointwise convergence to uniform convergence
    Posted in the Calculus Forum
    Replies: 13
    Last Post: November 29th 2009, 09:25 AM
  5. Pointwise Convergence vs. Uniform Convergence
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 31st 2007, 06:47 PM

Search Tags


/mathhelpforum @mathhelpforum