Results 1 to 2 of 2

Thread: Cauchy Test

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    28

    Cauchy Test

    For the series:

    $\displaystyle \sum_{n=1}^{\infty} \frac{1}{(n)^(1/2)(logn)^3}$

    To show it is divergent/convergent would you first apply the Cauchy test:

    $\displaystyle 2^n \frac{1}{(2^(n/2) (nlog(2)^)3}$


    $\displaystyle \frac{2^(n/2)}{(n^3 log(2)^3)}$

    Then apply the ratio test to get the lim = sqrt(2) so it is a divergent series?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    6
    Is easy to see that exists an $\displaystyle n_{0}$ such that $\displaystyle \forall n>n_{0}$ is...

    $\displaystyle \displaystyle \frac{1}{\sqrt{n}\ \ln^{3} n} > \frac{1}{n}$

    ... and then the series diverges...



    Merry Christmas from Italy

    $\displaystyle \chi$ $\displaystyle \sigma$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cauchy's convergence test
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Mar 15th 2011, 12:24 PM
  2. Cauchy condensation test
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Jun 22nd 2010, 11:34 AM
  3. cauchy condensation test
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Apr 25th 2010, 08:04 AM
  4. Cauchy's Root test
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Apr 22nd 2010, 02:46 AM
  5. Cauchy Condensation Test
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 29th 2008, 07:45 AM

Search Tags


/mathhelpforum @mathhelpforum