1. Not finding help here? Sign up for a free 30min 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!

General question about convergence of series

  1. May 14, 2005 #1
    In general, is it true that if a sequence has a limit that it converges and if it does not have a limit that it diverges?when i say have a limit i mean that the limit exists.
     
  2. jcsd
  3. May 14, 2005 #2
    Given [tex]\sum_{n=0}^{\infty} a_n[/tex]

    if the series converges, then

    [tex]\lim_{n\rightarrow\infty}a_n = 0[/tex]

    This does not mean that if the limit = 0 it converges, but that it has a possibility to converge. If the limit does not equal 0, the series diverges.
     
  4. May 14, 2005 #3

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Are you talking about sequences or series, RadiationX?

    By definition, if a sequence has a finite limit, then it converges to that limit.
     
  5. May 14, 2005 #4
    yes i was talking about sequences
     
  6. May 15, 2005 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes. "Converge" is DEFINED as "has a limit". "Diverge" is defined as "does not have a limit".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: General question about convergence of series
Loading...