Results 1 to 2 of 2

Math Help - Sequence Convergence

  1. #1
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19

    Sequence Convergence

    I want to find the limit of the sequence:

    a_n=(-1)^n\frac{n}{n+1}

    \lim_{n->\infty}a_n=\lim_{n->\infty}\mid (-1)^n \frac{n}{n+1} \mid

    \lim_{n->\infty}\frac{n}{n+1}

    =1

    My book says the sequence converges at -1.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,415
    Thanks
    1853
    Quote Originally Posted by adkinsjr View Post
    I want to find the limit of the sequence:

    a_n=(-1)^n\frac{n}{n+1}

    \lim_{n->\infty}a_n=\lim_{n->\infty}\mid (-1)^n \frac{n}{n+1} \mid
    This is NOT a_n. There is no absolute value in a_n.

    \lim_{n->\infty}\frac{n}{n+1}

    =1

    My book says the sequence converges at -1.

    Then both you and your book are wrong! For n= 10000000, say, a_{10000000}= (-1)^{10000000}\frac{10000000}{10000001}= 0.999999000, approximately, very close to 1 while if n= 1000001, a_{1000001}= (-1)^{1000001}\frac{1000001}{1000002}= -0.9999998, approximately, which is very close to -1.

    This sequence does not converge. It has a subsequence (n even) that converges to 1 and another (n odd) that converges to -1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: October 12th 2009, 11:10 AM
  2. Sequence Convergence
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 11th 2009, 07:07 AM
  3. Replies: 6
    Last Post: October 1st 2009, 10:10 AM
  4. Replies: 6
    Last Post: October 24th 2008, 02:45 PM
  5. Convergence of Sequence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 9th 2008, 07:48 AM

Search Tags


/mathhelpforum @mathhelpforum