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: 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


    User Avatar
    Science Advisor

    Yes. "Converge" is DEFINED as "has a limit". "Diverge" is defined as "does not have a limit".
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook