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Question about the Integral Test

  1. Apr 13, 2013 #1
    So this is my first post, I was wondering can you explain the first two examples of this page?

    http://www.math.ubc.ca/~rathb/mar_6_p_4.jpg [Broken]

    What I don't understand is why, if there is a horizontal asymptote at p = 0.99 < 1 on first example, it diverges to infinity but in the second example, there is also a horizontal asymptote at p = 1.01 > 1 but it converges?

    What's the difference and what concept am I not understanding here?

    Thanks!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 14, 2013 #2

    mathman

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    The convergence question is only distantly related to the asymptote.
    A series with terms 1/nx diverges for x ≤ 1 and converges for x > 1.

    The integral test shows this.
     
  4. Apr 14, 2013 #3
    Ah i realize this is simply a p-series representation. Thanks, that clears it up
     
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