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: Is there a differnt way to write this expression?

  1. Mar 7, 2010 #1
    f(z) = SUM [(-1)n

    Where SUM = sum from n=0 to infinity

    Looks to me like there isn't but there must be a simpler way to write that.

    Thanks
     
    Last edited: Mar 7, 2010
  2. jcsd
  3. Mar 7, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It's divergent, isn't? The nth term doesn't approach 0.
     
  4. Mar 7, 2010 #3
    The question is to write this power series as a function

    2hn01gp.jpg
     
    Last edited: Mar 7, 2010
  5. Mar 7, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    z^(2n)/n! isn't equal to e^(z^2). The SUM of the series z^(2n)/n! is e^(z^2). That would be fine if the (-1)^n weren't there. Can't you think of a function that's a lot like e^(z^2) that will give you the alternating sign in the series?
     
  6. Mar 7, 2010 #5
    I just keep getting into the routine of trying to simply it like before. Do you mean replace e^(z^2) or multiply in some function f(z)/f(z)?
     
  7. Mar 7, 2010 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    (-1)^n*z^(2n). Can you think of a way to write that as r^n for some number r? What would r be?
     
  8. Mar 7, 2010 #7
    ahh yes
     
    Last edited: Mar 7, 2010
  9. Mar 7, 2010 #8
    For the 2nd part I have it down to

    z-2 SUM (-1)n.(z2/4)n+1

    Is there anyway I can progress from here or should I go back and try a different way?
     
  10. Mar 7, 2010 #9

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It's a geometric series.
     
  11. Mar 7, 2010 #10
    (z2/4)n+1 starting at n=0

    = 1/(1-z2/4) - 1

    => Series = z-2 SUM (-1)n/(1-z2/4) + (-1)n+1
     
  12. Mar 7, 2010 #11

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You just did the same wrong thing you did in the first problem. You replaced a term is the series with the sum of a series. And you missed the cue to do the same thing you did with the (-1)^n in the first problem. You series has the form a*r^n. r just might have a (-1) in it.
     
  13. Mar 7, 2010 #12
    ah yes, i have my r now thanks, was simple after that!

    Thanks alot
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook