Results 1 to 2 of 2

Math Help - Sequences, Series and Convergence.

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    109

    Sequences, Series and Convergence.

    For each of the following sequences, determine the convergence or divergence. If the sequence converges, find it's limit:

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

    2) { {a_n}}  = { {\frac{3n^{-1} - 5n^{2}}{2n(7n-9n^{-2})}}}


    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,656
    Thanks
    1480
    Quote Originally Posted by qzno View Post
    For each of the following sequences, determine the convergence or divergence. If the sequence converges, find it's limit:

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

    2) { {a_n}}  = { {\frac{3n^{-1} - 5n^{2}}{2n(7n-9n^{-2})}}}


    Thanks!
    Do you want to know if the sequences converge or if the series converge?


    1. The sequence a_n = 1 + \frac{(-1)^n}{n} is clearly convergent.

    As n \to \infty, \frac{(-1)^n}{n} \to 0.

    Therefore a_n \to 1


    2. The sequence a_n = \frac{3n^{-1} - 5n^{2}}{2n(7n-9n^{-2})} can be rewritten as

    a_n = -\frac{5}{14} - \frac{1}{7n^2 - 9}.


    As n \to \infty, \frac{1}{7n^2 - 9} \to 0.


    Therefore

    a_n \to -\frac{5}{14}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sequences, convergence
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 2nd 2011, 02:37 AM
  2. Convergence in sequences of sequences
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: October 19th 2010, 07:28 AM
  3. Replies: 4
    Last Post: December 1st 2009, 03:23 PM
  4. Replies: 9
    Last Post: May 31st 2009, 09:51 AM
  5. Replies: 3
    Last Post: May 15th 2009, 11:54 AM

Search Tags


/mathhelpforum @mathhelpforum