Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Converge, absolutely or conditionally?

  1. Jan 24, 2007 #1
    1. The problem statement, all variables and given/known data

    does it converge absolutely, converge conditionally, or diverge?

    heres the equation: http://img219.imageshack.us/img219/4645/untitled29fy.jpg [Broken]

    2. Relevant equations


    3. The attempt at a solution

    looks like the sin equation converges to zero.

    i think this is an alternating series, but i'm not sure if this part converges or diverges?

    thanks for any help here.
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Jan 24, 2007 #2

    Gib Z

    User Avatar
    Homework Helper

    Yep, The terms converge to zero, and it converges absolutely, and therfore also with the alternating series.
  4. Jan 24, 2007 #3
    Great, thanks again.

    ..also, the alternating series must approach 0, in order to converge right?

    ..and, in this problem, sin(pi/anything) will always be 0, correct?
    Last edited: Jan 24, 2007
  5. Jan 24, 2007 #4

    Gib Z

    User Avatar
    Homework Helper

    Ahh no, if anything was a constant that it wont be zero.
  6. Jan 24, 2007 #5


    User Avatar
    Science Advisor
    Homework Helper

    No ... but sin(pi*n) is always 0 when n is an integer. Maybe that's what you were thinking of (though it doesn't seem relevant to this question).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook