October 26th, 2013, 11:40 AM  #1 
Newbie Joined: Mar 2013 Posts: 24 Thanks: 0  Nth term test for series
The series is the sum of (3 * ?n) / ln(9n) where n = 2 and goes to infinite. So far, we've only be taught to do the integral test, Nth term test, and to check for geometric or telescopic series. The only on that applies here is the Nth term test, but after working it out, I found the lim(n > inf) of the Nth term to be 0, meaning it is indeterminate from this test. Can anyone help me understand why this is series is divergent? 
October 26th, 2013, 01:00 PM  #2  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Nth term test for series Quote:
 
October 26th, 2013, 01:38 PM  #3 
Newbie Joined: Mar 2013 Posts: 24 Thanks: 0  Re: Nth term test for series
Okay, so is this the correct usage of L'Hopital's rule? Because the first time I did the problem I used L'Hopital's again after simplifying to: or something like that. 
October 26th, 2013, 02:12 PM  #4  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Nth term test for series Quote:
Quote:
 

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