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

  • Thread starter Randall
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  • #1
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Homework Statement


Use the integral test to determine if this series converges or diverges: sum from n=1 to infinity of n/(1+(n^2))

Homework Equations


Integral test: a series and it's improper integral both either converge or both diverge

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.
 

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Answers and Replies

  • #2
B3NR4Y
Gold Member
170
8
Your proof that it is positive and decreasing isn't sufficient, but the integral is fairly trivial. U-substitution comes to mind.
 
  • #3
22
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Thank you! Yes I used substitution and got it to work :)
 

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