Results 1 to 2 of 2

Math Help - Find the value of p for the convergent series.

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    92

    Find the value of p for the convergent series.

    <br /> <br />
\sum\limits_{n = 1}^\infty  {ln (n) / n^{ p} }<br />

    I am using integral test as t goes to infinity. I am not familiar with finding the p

    Any help.
    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
    The sum has to be compared with the integral...

    \int_{1}^{\infty} \frac{\ln x}{x^{p}}\cdot dx (1)

    Integrating by parts we have...

    \int_{1}^{\infty} \frac{\ln x}{x^{p}}\cdot dx = \frac{1}{-p+1}\cdot \{|x^{-p+1}\cdot \ln x|_{1}^{\infty} - \int_{1}^{\infty} \frac{dx}{x^{p}} \} (2)

    Observing (2) we it is evident that integral (1) will converge only if p>1, and the same is for the series \sum_{n=1}^{\infty} \frac{\ln n}{n^{p}}...

    Kind regards

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

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: December 12th 2009, 05:08 PM
  2. Replies: 3
    Last Post: April 6th 2009, 11:03 PM
  3. Find the sum of the convergent series?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 1st 2008, 11:19 PM
  4. find convergent set of the power series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 31st 2007, 05:06 PM
  5. find convergent set of the power series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 31st 2007, 06:47 AM

Search Tags


/mathhelpforum @mathhelpforum