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Does the limit converge or diverge

  • Thread starter kuczmama
  • Start date
  • #1
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Homework Statement


infinity
Ʃ [itex]\frac{ln(n)}{n\sqrt{n}}[/itex]
n=1

Homework Equations


I think that I need to use either the limit comparison test or the ratio test.


The Attempt at a Solution



After listing all the terms I found out that the function was positive and decreasing, and that the terms approached 0. However when I used the limit comparison test or the root test I keep on getting an answer of infinity or 0, which is inconclusive. So I don't know how else to approach the problem. Is there something easy that I am overlooking. Thanks.
 
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Answers and Replies

  • #2
33,284
4,989

Homework Statement


infinity
Ʃ [itex]\frac{ln(n)}{n\sqrt{n}}[/itex]
n=1

Homework Equations


I think that I need to use either the limit comparison test or the ratio test.


The Attempt at a Solution



After listing all the terms I found out that the function was positive and decreasing, and that the terms approached 0. However when I used the limit comparison test or the root test I keep on getting an answer of infinity or 0, which is inconclusive. So I don't know how else to approach the problem. Is there something easy that I am overlooking. Thanks.
Show us what you tried for the limit comparison test. I agree that the ratio test would not be conclusive.
 
  • #3
382
4
I think the best test to use is the ratio test:

If there exists a constant C < 1 such that |an+1/an|<C for all sufficiently large n, then ∑an converges absolutely.
 
  • #4
LCKurtz
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Have you thought about the integral test?
 
  • #5
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for the limit comparison test I tried a bunch of different comparisons. I said as lim n-> infinity of

lim n→∞. of (ln(n)/(nsqrt(n))/(1/n^5/4).That didnt give me any help. Then I tried comparing it to 1/n^1/4. Then I tried comparing it to a bunch of other stuff but nothing seemed to work. I cant figure out what to do
 
  • #6
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Also I never thought about the integral test. I will try that
 
  • #7
LCKurtz
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@kuczmama: Don't use the X2 key inside tex brackets. Right click on this to see how to do exponents:

[tex]n^{\frac 3 2}[/tex]
 
  • #8
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I got that the integral converges to 4. I guess that this means the sum also converges. Thanks alot guys!!
 

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