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Please help me with this series test. Thank you.

  1. Apr 25, 2015 #1
    https://lh3.googleusercontent.com/z468bYHn_-Ufcp0M_XFbTgUtEL2qDzNUZSRgjU3Qz8ZcFj8pMg5k7Ip9i9EejHNPdBQc3EltXrAI2Ck=w1342-h587
     
  2. jcsd
  3. Apr 25, 2015 #2

    micromass

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    Just because the ##n##th term converges to ##0##, doesn't mean the series converges. Unless you can explain better why it might imply this in this case.
     
  4. Apr 25, 2015 #3

    micromass

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    And the ##p##-test only works for positive series (a series whose terms are positive).
     
  5. Apr 25, 2015 #4
    That's what I think of. Also how do you know when to test for absolute converges and conditional converges? Thank you for trying to help.
     
  6. Apr 25, 2015 #5

    Mark44

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    Instead of answering that question, I think it would be a good idea for you to step back and take a closer look at the two tests you used, the p-series test and what you call the "nth term test."
    As already stated, the p-series applies only to series consisting of positive terms. You also misused the other test that you used. What exactly does that test say?
     
  7. Apr 26, 2015 #6

    HallsofIvy

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    If a series "converges absolutely" then there is no point in asking if it converges conditionally. So it would seem to make sense to first try to show that a series converges absolutely and only if it doesn't try to show that it converges conditionally.

    One test you do not mention is the "alternating sequence test": if, for [itex]a_n> 0[/itex], [itex]\lim_{n\to 0} a_n= 0[/itex] then [itex]\sum (-1)^n a_n[/itex] converges.
     
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