Results 1 to 2 of 2

Math Help - Test the following series for convergence..

  1. #1
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    562

    Test the following series for convergence..

    \sum_{n=1}^{\infty} \dfrac{1}{n^{sinh(n)}}
    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
    5
    Because is \sinh 1 = 1.1752011936438... and the function \sinh (*) is [strongly] increasing, for all n will be...

    \frac{1}{n^{\sinh n}} < \frac{1}{n^{1.1}} (1)

    Now the series...

    \sum_{n=1}^{\infty}\frac{1}{n^{1.1}} (2)

    ... converges so that...

    Kind regards

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

Similar Math Help Forum Discussions

  1. Test the convergence of the series
    Posted in the Calculus Forum
    Replies: 9
    Last Post: December 23rd 2009, 02:06 AM
  2. Convergence test for two series
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: September 9th 2009, 01:11 PM
  3. series convergence test and sum?
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 22nd 2009, 07:53 AM
  4. Test the Convergence of the series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 23rd 2008, 03:39 PM
  5. Series convergence test
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 2nd 2008, 06:51 PM

Search Tags


/mathhelpforum @mathhelpforum