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Homework Help: Alternating Series Test for Convergence

  1. Jun 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Does this series converge absolutely or conditionally?

    2. Relevant equations

    Series from n=1 to ∞ (-1)^(n+1) * n!/2^n

    3. The attempt at a solution

    In trying to apply the alternating series test, I have found the following:

    1.) n!/2^n > 0 for n>0
    2.) Next, in testing to see if n!/2^n is decreasing, I found that (n!/2^n)/((n+1)!/2^(n+1)) < 1 for n large.

    Stopping here, this suggests the series diverges in its original form. Is this correct? Thank you!
  2. jcsd
  3. Jun 28, 2012 #2


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    Science Advisor
    Homework Helper
    Gold Member

    You have apparently shown the terms of the series are increasing for n large, so they don't go to zero. So yes, you are correct that the series diverges.
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