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!

Series Comparison Test, help?

  1. Apr 20, 2012 #1
    Series Comparison Test, URGENT help?

    Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed.

    1. For all n>2, ∑ 1/ (n^2−1) < 1/n^2 so converges
    2. For all n> 1, ∑ arctan(n) / n^3 < pi / 2n^3 so converges
    3. For all n>1, ∑ ln(n)/n^2 < 1/n^1.5 so converges
    4. For all n>1, ∑ 1/nln(n) < 2/n so diverges
    5. For all n>2, ∑ n/(n^3 - 8) < 2/n^2 so converges
    6. For all n>2, ∑ ln(n)/n > 1/n so diverges

    I belive (1) is incorrect.
    (2), (3), and (6) I believe are correct.
    But I can't figure out 4 and 5 ? I think 4 is incorrect but i'm not sure, and for 5 shouldn't it be compared to 1/n^2 ?

    Please help!
     
    Last edited: Apr 20, 2012
  2. jcsd
  3. Apr 20, 2012 #2
    Re: Series Comparison Test, URGENT help?

    What's your reasoning behind the numbers you have answers for?
     
  4. Apr 20, 2012 #3
    Re: Series Comparison Test, URGENT help?

    for (1) 1/n^2 is actually greater than 1/ (n^2−1), for (4) if it diverges it should actually be asubn > bsubn not the other way around, and (5) the bsubn should be n/n^3 which becomes 1/n^2

    for the (2),(3) 1/ n^p where p>1 so it converges which is correct, and for (6) n^p, here p=1 so it diverges which is correct.
     
  5. Apr 20, 2012 #4
    Re: Series Comparison Test, URGENT help?

    Your reasoning for 1 is correct (the same reasoning applies to 5; that one has the inequality in the wrong direction).
    2, 3, and 4 are correct too.
     
  6. Apr 20, 2012 #5
    Re: Series Comparison Test, URGENT help?

    thank you for your help,
    so I just wanted to make sure, for my answers:

    1. incorrect
    2. correct
    3. correct
    4. incorrect
    5. incorrect
    6. correct

    is this okay?
     
  7. Apr 20, 2012 #6
    Re: Series Comparison Test, URGENT help?

    Looks good :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Series Comparison Test, help?
  1. Series Comparison Test (Replies: 2)

Loading...