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October 26th, 2013, 11:40 AM   #1
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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?
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October 26th, 2013, 01:00 PM   #2
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Re: Nth term test for series

Quote:
Originally Posted by Polaris84
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?
The sequence diverges!
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October 26th, 2013, 01:38 PM   #3
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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.
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October 26th, 2013, 02:12 PM   #4
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Re: Nth term test for series

Quote:
Originally Posted by Polaris84
Okay, so is this the correct usage of L'Hopital's rule?

Yes

Quote:
Originally Posted by Polaris84

Because the first time I did the problem I used L'Hopital's again after simplifying to:

Should have been:

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