1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook