Results 1 to 3 of 3

Thread: Series question

  1. #1
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106

    Series question

    $\displaystyle \sum(-1)^{n}\frac{1+n}{n^{2}-n}$

    in the sum n=2 and goes to infinity

    so is the sequence divergent, conditionally convergent or absolutely convergent?

    so I chose conditionally convergent because of the (-1)^n

    but the limit comparison test tells me that the series is divergent since 1/n is divergent....so does this problem work out?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
    Posts
    802
    Hi

    The limit comparison test only apply for series with positive terms, the only things you might get is that $\displaystyle \sum \frac{1+n}{n^2-n}$ is divergent.

    so I chose conditionally convergent because of the (-1)^n
    It's not because there is $\displaystyle (-1)^n$ that the series satisfy the alternating test. (you also need to show that $\displaystyle \frac{1+n}{n^2-n} $ decreases and that $\displaystyle \lim_{n\to \infty}\frac{1+n}{n^2-n}=0$)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by akhayoon View Post
    $\displaystyle \sum(-1)^{n}\frac{1+n}{n^{2}-n}$

    in the sum n=2 and goes to infinity

    so is the sequence divergent, conditionally convergent or absolutely convergent?

    so I chose conditionally convergent because of the (-1)^n

    but the limit comparison test tells me that the series is divergent since 1/n is divergent....so does this problem work out?
    Two words...Ratio test
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. question about answer to fourier series question
    Posted in the Advanced Math Topics Forum
    Replies: 11
    Last Post: Feb 9th 2011, 12:29 PM
  2. Replies: 0
    Last Post: Jan 26th 2010, 08:06 AM
  3. Series Question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 28th 2008, 12:44 AM
  4. Sequences and Series - Power Series Question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Apr 20th 2008, 07:32 PM
  5. Replies: 6
    Last Post: Aug 18th 2007, 12:13 PM

Search Tags


/mathhelpforum @mathhelpforum