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Alternate series question

  1. Mar 15, 2005 #1
    I'm reviewing power series for use in differential equations and I'm having some trouble remembering how to deal with alternating series.

    For instance, if I have:

    if [tex]a_n=(\frac{3}{2})^n[/tex]
    This fails the alternate series test because the limit of [tex]a_n[/tex] as n goes to infinity doesn't equal 0.

    Can I group the (-1)^n into the fraction and call it a geometric series? In that case, it would diverge, |r| would be greater then 1.
  2. jcsd
  3. Mar 15, 2005 #2


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    Yes, both ways are fine.
  4. Mar 15, 2005 #3
    thanks for the help.
  5. Mar 15, 2005 #4
    If the summand doesn't go to zero, the series cannot converge, regardless of whether it is alternating or not (using the most common definition of convergence).
  6. Mar 15, 2005 #5


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    Yes, you're right. This is the best way to solve the problem. The summand doesn't go to zero so the series diverges.
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