Results 1 to 3 of 3

Thread: Conditional and absolute convergence

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    15

    Conditional and absolute convergence

    For each $\displaystyle y \in (0,1]$, find a series of the form $\displaystyle \sum\limits_{n=1}^{\infty}{a_nn^{-x}}$ which is absolutely convergent for $\displaystyle x>1$ but not for $\displaystyle x<1$ and is (conditionally) convergent for $\displaystyle x>y$ but not for $\displaystyle x<y$.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    22
    Quote Originally Posted by Newtonian View Post
    For each $\displaystyle y \in (0,1]$, find a series of the form $\displaystyle \sum\limits_{n=1}^{\infty}{a_nn^{-x}}$ which is absolutely convergent for $\displaystyle x>1$ but not for $\displaystyle x<1$ and is (conditionally) convergent for $\displaystyle x>y$ but not for $\displaystyle x<y$.
    Is the sequence supposed to depend on $\displaystyle y$?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    15
    Yes; we may assume we're given a $\displaystyle y \in (0,1]$ and we want to find a series as stated (by defining $\displaystyle a_n$, which are allowed to depend on the given $\displaystyle y$).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. determine convergence, absolute or conditional
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Apr 10th 2011, 03:32 AM
  2. Absolute or conditional convergence question
    Posted in the Calculus Forum
    Replies: 13
    Last Post: Feb 5th 2010, 10:42 AM
  3. Absolute or conditional convergence
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Mar 31st 2009, 08:15 PM
  4. Absolute and conditional convergence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jan 25th 2009, 02:57 PM
  5. absolute or conditional convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 16th 2008, 11:29 AM

Search Tags


/mathhelpforum @mathhelpforum