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Series (p-series)

  1. Dec 9, 2009 #1
    if my an = 1 / (n+1)^2
    can i use p series test to confirm that the series will converge..
    where p = 2..
     
  2. jcsd
  3. Dec 9, 2009 #2

    Mark44

    Staff: Mentor

    Sure. If your series is something like this,
    [tex]\sum_{n = 0}^{\infty} \frac{1}{(n + 1)^2}[/tex]

    you can change the series index to write the series this way:
    [tex]\sum_{n = 1}^{\infty} \frac{1}{n^2}[/tex]
     
  4. Dec 9, 2009 #3
    it's comparison test right?
    the series will converge..
    am i right?
     
  5. Dec 9, 2009 #4
    p-series converge for p>1, so yes, your summation converges.
     
  6. Dec 9, 2009 #5

    Mark44

    Staff: Mentor

    You don't need the comparison test if you know the p-series test, and this is a p-series.
     
  7. Dec 10, 2009 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I believe that naspek was saying that he can argue that [itex]1/(n+1)^2< 1/n^2[/itex] and so use the comparison test without using your idea of changing the index.
     
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