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Homework Help: Convergence of Infinite Series

  1. Nov 26, 2007 #1
    Question: Test for convergence:


    (the sum is from 1 to infinity)

    I tried using


    and showing that either the first one was convergent or the last one was divergent using various tests but didn't get anywhere.

    Any hints?
  2. jcsd
  3. Nov 26, 2007 #2
    Try using the Ratio Test. That's what I first try to do anytime I see n!
  4. Nov 26, 2007 #3
    Ratio Test:


    Since that's more than 1 as n goes to infinity it diverges. Am I right?
  5. Nov 26, 2007 #4
    I did a bunch of these. I need to get a good grade so I will just post them up here with my answers and if I got one wrong please just let me know to look over it again.

    1. [tex]\sum\frac{1}{ln(n)}[/tex] (sum from 2 to inf.) diverges

    b/c 1/ln(n)>1/n which diverges

    2. [tex]\sum\frac{1}{2n(2n+1)}[/tex] converges

    b/c 1/n^2 converges

    3. [tex]\sum\frac{1}{(n(n+1))^{.5}}[/tex] diverges

    b/c 1/n diverges and then limit comparison test to show this diverges too.

    4. [tex]\sum\frac{1}{2n+1}[/tex] diverges

    b/c 1/2n diverges and then limit comparison to show this diverges too.

    I'd really appreciate it if somebody could check me on these. Thanks.
  6. Nov 26, 2007 #5


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    Those all look right to me
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