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!

Alternating Series Help

  1. Nov 21, 2005 #1
    I apologize right now for the fact that I have no idea how to use LaTeX

    I can't figure out if the following alternating series is convergent or not:

    Sum(((-1)^(n-1)) * ((2n+1)/(n+2))) from 1 to infinity

    the root test is not applicable, A(n+1)>An, and the ratio test gives me Limit=1, so I have no comclusive evidence either way. Even Maple 10 couldnt give me an answer.
    I have a test tomorrow. HELP!!!!!!!
  2. jcsd
  3. Nov 21, 2005 #2
    Did you try the alternating series test?
  4. Nov 21, 2005 #3


    User Avatar
    Science Advisor

    Just take a look at the limiting terms in that series. As n goes to infinity the absolute value of the terms goes to two, so alternating or not there is no way it can converge.
  5. Nov 21, 2005 #4


    User Avatar
    Science Advisor

    BYW. I'm petty sure you can show that the above series is bounded, that is that it doesn't creep off to +/- infinity, but it definitely doesn't converge to a well defined limit point.
  6. Nov 22, 2005 #5


    User Avatar
    Science Advisor

    You are aware, are you not, that is an does not go to zero, then the series[itex]\Sigma a_n[/itex] cannot converge? That's normally the very first "series" property you learn!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Alternating Series Help
  1. Help with a series (Replies: 12)

  2. Limit of a series help (Replies: 4)