1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted