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- Please help - easy series

  1. Nov 5, 2007 #1
    URGENT - Please help - easy series

    How can I show that the series from 1 to infinity of

    (-1)^(n+1) * n / sqrt(n^(2)+2) diverges instead of converging abs/conditionally?



    Also, for the series from 1 to infinity of:

    (-1)^(n+1)/(2)^(1/n)


    I applied the root test and came out with:

    lim n --> infinity of 1^n/2 = 1/2


    yet, the answer key says the series diverges...can anyone explain this?
     
    Last edited: Nov 5, 2007
  2. jcsd
  3. Nov 5, 2007 #2

    Dick

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    The nth term of either of those series doesn't even converge to zero.
     
  4. Nov 5, 2007 #3
    try the alternating series test.
     
  5. Nov 5, 2007 #4
    if you just try to simplify and do the limits the denomintor goes to 1 and the top alternates from -1 to 1 and back and forth.
     
  6. Nov 5, 2007 #5

    Dick

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    Well, yeah. Isn't that what I said?
     
  7. Nov 5, 2007 #6
    I see, the limit of 1/(2)^1/n goes to 1, so it fails to go to 0 and hence diverges.

    and the first can be simplified to n/n = 1, which doesn't go to 0, so it diverges...

    Is it that simple?
     
  8. Nov 5, 2007 #7

    Dick

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    It is that simple. When are applying a test like the alternating series test, make sure that ALL of the premises apply. Of course, just because a test doesn't apply, doesn't make the series diverge. But any series that for large n looks like +1,-1,+1,-1... does not converge.
     
    Last edited: Nov 6, 2007
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