Results 1 to 2 of 2

Math Help - Integral Test

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    30

    Integral Test

    Trying to determine whether the following series converges or diverges using the intergral test:

    \sum _{n=1}^{\infty }{\frac {1}{n\ln  \left( n+1 \right) }}

    I know the theory of how to use the integral test but im struggling to get this into an easily integratable form. I tried using substitution like y=ln(n+1) etc. but could get anywhere. Any ideas?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
    Can we use comparison test before using integral test ? ie  \frac{1}{n} > \frac{1}{n+1} and

     \sum_{n=1}^{\infty} \frac{1}{n \ln(n+1)} >\sum_{n=1}^{\infty} \frac{1}{(n+1)\ln(n+1)} = \sum_{n=2}^{\infty} \frac{1}{n \ln(n)}

    and we have  \int \frac{dx}{ x \ln{x} } = \ln{\ln{x}} + C
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. integral test help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 23rd 2011, 07:33 PM
  2. Integral Test and comparison test help!
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 3rd 2009, 09:46 PM
  3. integral test help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 27th 2009, 12:16 AM
  4. Integral Test/Comparison Test
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 27th 2009, 10:58 AM
  5. integral test
    Posted in the Calculus Forum
    Replies: 11
    Last Post: January 13th 2009, 02:56 PM

Search Tags


/mathhelpforum @mathhelpforum