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: Alternate series question

  1. Mar 15, 2005 #1
    I'm reviewing power series for use in differential equations and I'm having some trouble remembering how to deal with alternating series.

    For instance, if I have:
    [tex]\sum(-1)^n(\frac{3}{2})^n[/tex]

    if [tex]a_n=(\frac{3}{2})^n[/tex]
    This fails the alternate series test because the limit of [tex]a_n[/tex] as n goes to infinity doesn't equal 0.

    Can I group the (-1)^n into the fraction and call it a geometric series? In that case, it would diverge, |r| would be greater then 1.
     
  2. jcsd
  3. Mar 15, 2005 #2

    learningphysics

    User Avatar
    Homework Helper

    Yes, both ways are fine.
     
  4. Mar 15, 2005 #3
    thanks for the help.
     
  5. Mar 15, 2005 #4
    If the summand doesn't go to zero, the series cannot converge, regardless of whether it is alternating or not (using the most common definition of convergence).
     
  6. Mar 15, 2005 #5

    learningphysics

    User Avatar
    Homework Helper

    Yes, you're right. This is the best way to solve the problem. The summand doesn't go to zero so the series diverges.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...