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Rudin's principles of mathematical analysis

  1. Mar 19, 2008 #1
    1. The problem statement, all variables and given/known data
    Does anyone have this book? I have some questions about chapter 3.


    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Mar 19, 2008
  2. jcsd
  3. Mar 19, 2008 #2

    quasar987

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    Try to find an expression for the Nth partial sum.

    This is an example of what is called a "telescoping series".
     
  4. Mar 19, 2008 #3
    Yes I figured that out before you posted and deleted that part of the post because it was embarrassing.

    What about [itex]\sum_n \frac{\sqrt{n+1}-\sqrt{n}}{n} [/itex]. This definitely does not telescope. But both 1/n and \sqrt{n+1}-\sqrt{n} diverge so it is pretty clear that their product will. But what test should I use? The ratio test is too hard too evaluate. The root test is even harder to evaluate. What series can I compare it to?
     
    Last edited: Mar 20, 2008
  5. Mar 20, 2008 #4

    NateTG

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    Hmm, is any term in that series larger than:
    [tex]\frac{1}{2n^{\frac{3}{2}}}[/tex]

    (This falls out easily with a little algebra.)
     
  6. Mar 20, 2008 #5
    No (but I am not sure why you have the 2 there).

    So, does anyone have the book?
     
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