(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: Alternating Series Test for Convergence

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