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Proving Convergence of this

  • Thread starter simba924
  • Start date
  • #1
3
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Homework Statement



[tex]\sum[/tex] from n=2 to [tex]\infty[/tex] of n/((n2-5)*(ln n)2)

Homework Equations





The Attempt at a Solution


I've tried Limit Comparison but I always get a limit of 0 which will not work. Ratio test doesn't help. I don't think a direct comparison can be made but that seems to be the only other option...

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
316
0
Hi simba924!

To simplify the problem a bit, show that

[tex]\frac{n}{n^2-5}\le\frac{2}{n}[/tex]

for large n. Then apply the http://en.wikipedia.org/wiki/Integral_test_for_convergence" [Broken].
 
Last edited by a moderator:
  • #3
3
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Ahh thanks. Can you explain that in a little more detail though, I don't really get it.
 
  • #4
3
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Hey I still need some help with this one. I'm pretty sure that [tex]\sum[/tex] 2/n is not convergent because it is in form integer/np where p=1

Can anyone help?
 
  • #5
316
0
Hey I still need some help with this one. I'm pretty sure that [tex]\sum[/tex] 2/n is not convergent because it is in form integer/np where p=1

Can anyone help?
Remember, you still have the additional factor 1/(ln n)^2 (without which it would diverge). To do the integral test you have to check that

[tex]\int_2^{\infty}\frac{1}{x(\log(x))^2}[/tex]

exists (you can find an explicit antiderivative, Hint: substitution).
 

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