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Use the integral test to determine if this series converges or diverges

  1. Jan 2, 2015 #1
    1. The problem statement, all variables and given/known data
    Use the integral test to determine if this series converges or diverges: sum from n=1 to infinity of n/(1+(n^2))
    2. Relevant equations
    Integral test: a series and it's improper integral both either converge or both diverge

    3. The attempt at a solution
    see attached - I need help finding the integral. I tried using an online integral calculator, symbolab but it says there is no integral. I'm guessing there is some way to split this up into pieces that I'm not seeing. Please help.

    Attached Files:

  2. jcsd
  3. Jan 2, 2015 #2


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    Gold Member

    Your proof that it is positive and decreasing isn't sufficient, but the integral is fairly trivial. U-substitution comes to mind.
  4. Jan 2, 2015 #3
    Thank you! Yes I used substitution and got it to work :)
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